{"id":128435,"date":"2023-09-13T15:57:00","date_gmt":"2023-09-13T10:27:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=128435"},"modified":"2023-11-21T11:07:39","modified_gmt":"2023-11-21T05:37:39","slug":"rd-sharma-class-10-solutions-chapter-15-exercise-15-4","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-15-exercise-15-4\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.4 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-128447\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.4.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.4.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.4-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4:&nbsp;<\/strong>This exercise includes problems involving calculating the area of such plane figure combinations. Students can use the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Class 10 Solutions<\/strong><\/a> provided by experts at Kopykitab to get complete solutions to all exercise problems. Students can also download the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-15-areas-related-to-circles\/\"><strong>RD Sharma Solutions for Class 10 Maths Chapter 15<\/strong><\/a> Areas Related To Circles Exercise 15.4 PDF.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d907b44c524\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" 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id=\"download-rd-sharma-class-10-solutions-chapter-15-exercise-154-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-15-Exercise-15.4.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-15-Exercise-15.4.pdf\">RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-15-exercise-154-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 15 Exercise 15.4- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 1.<br>A plot is in the form of a rectangle ABCD having a semi-circle on BC as shown in the figure. If AB = 60 m and BC = 28 m, find the area of the plot.<br><img src=\"https:\/\/farm5.staticflickr.com\/4847\/43860743980_672de11f93_o.png\" alt=\"RD Sharma Class 10 Chapter 15 Areas related to Circle\" width=\"320\" height=\"157\"><br>Solution:<br>The plot is formed of a rectangle ABCD and one semicircle on BC as the diameter<br>\u2234 AB (l) = 60 m,<br>BC (b) = 28 m<br>\u2234 Radius of semicircle (r) =&nbsp;12&nbsp;BC<br>=&nbsp;12&nbsp;x 28 = 14m<br>Area of plot = area of rectangle ABCD + area of semicircle<br><img src=\"https:\/\/farm2.staticflickr.com\/1926\/43860743950_5254244af5_o.png\" alt=\"Areas related to Circles Class 10 RD Sharma\" width=\"134\" height=\"50\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4857\/43860743810_bf8844d4e8_o.png\" alt=\"RD Sharma Class 10 Chapter 15 Areas related to Circle\" width=\"236\" height=\"136\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 2.<br>A playground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added to its outside. If the sides of the rectangle are 36 m and 24.5 m, find the area of the playground. (Take \u03c0 = 22\/7).<br>Solution:<br>Length of rectangle (l) = 36 m 49<br>and width (b) = 24.5 = 492&nbsp;m<br><img src=\"https:\/\/farm5.staticflickr.com\/4814\/43860743600_fcb50f6607_o.png\" alt=\"Areas related to Circles Class 10 RD Sharma\" width=\"348\" height=\"555\"><br>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 3.<br>Find the area of the circle in which a square of area 64 cm2 is inscribed. (Use \u03c0 = 3.14)<br>Solution:<br>Area of square = 64 cm\u00b2<br>\u2234 Side of square =&nbsp;Area\u2212\u2212\u2212\u2212\u221a =&nbsp;64\u2212\u2212\u221a = 8 cm<br>\u2235 The square is inscribed in the circle<br>\u2234 The radius of the circle will be = 12 diagonal of<br>the square (r)=12&nbsp;x&nbsp;2\u2013\u221aa =&nbsp;12&nbsp;x&nbsp;2\u2013\u221a&nbsp;x 8 cm = 42\u2013\u221a<br>\u2234&nbsp;Area of the circle = \u03c0r\u00b2<br>= 3.14 x (412&nbsp;x&nbsp;2\u2013\u221a&nbsp;x 8 cm = 42\u2013\u221a)\u00b2 cm\u00b2<br>= 3.14 x 32 = 100.48 cm\u00b2<\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 4.<br>A rectangular piece is 20 m long and 15 m wide. From its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.<br>Solution:<br>Length of rectangular piece (l) = 20 m<br>and width (b) = 15m<br><img src=\"https:\/\/farm5.staticflickr.com\/4865\/43860743360_3687daa8eb_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles\" width=\"370\" height=\"234\"><br>Radius of each quadrant (r) = 3.5 m =&nbsp;72&nbsp;m<br>Now area of the rectangle = l x b = 20 x 15 = 300 m\u00b2<\/p>\n<p><br>an area of 4 quadrants = 4 x 14 \u03c0r\u00b2<br><img src=\"https:\/\/farm5.staticflickr.com\/4840\/43860743290_5013c6aa5d_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.4\" width=\"336\" height=\"170\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 5.<br>In the figure, PQRS is a square of side 4 cm. Find the area of the shaded square.<\/p>\n<p><img src=\"https:\/\/farm2.staticflickr.com\/1956\/43860743230_28c9a2fc0a_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles\" width=\"272\" height=\"250\"><br>Solution:<br>Side of the square PQRS (a) = 4 cm<br>\u2234 Area of total square = a\u00b2 = 4\u00d74=16 cm\u00b2<br>The radius of each of the four quadrants at the corners = 1 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1964\/43860743100_f5ec535d95_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.4\" width=\"340\" height=\"211\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 6.<br>Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed? (See figure)<br><img src=\"https:\/\/farm5.staticflickr.com\/4888\/43860743030_07ccd08be3_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"204\" height=\"186\"><br>Solution:<br>side of square (a) = 50 m<br>\u2234 Area of the square field = a\u00b2 = (50)\u00b2 m\u00b2 = 2500 m\u00b2<br>The radius of each quadrant (r) = 502 = 25 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4835\/43860742920_1e05974946_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"338\" height=\"422\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 7.<br>A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m x 16 m, find the area of the field in which the cow can graze. [NCERT Exemplar]<br>Solution:<br>Let ABCD be a rectangular field of dimensions 20 m x 16 m.<br>Suppose, a cow is tied at point A. Let the length of rope AE = 14m =r (say).<br><img src=\"https:\/\/farm5.staticflickr.com\/4841\/43860742850_89d4131e30_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"350\" height=\"472\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 8.<br>A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in the area of the grassy lawn in which the calf can graze. [NCERT Exemplar]<br>Solution:<br>Let the calf be tied at the corner A of the square lawn.<br><img src=\"https:\/\/farm2.staticflickr.com\/1964\/43860742740_571c7b989d_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 15 Areas related to Circles\" width=\"202\" height=\"190\"><br>Then, the increase in area = Difference of the two sectors of central angle 90\u00b0 each and radii 11.5 m (6 m + 5.5 m) and 6 m, which is the shaded region in the figure.<br><img src=\"https:\/\/farm2.staticflickr.com\/1940\/43860742680_18568b83fe_o.png\" alt=\"Learncbse.In Class 10 Chapter 15 Areas related to Circles\" width=\"288\" height=\"171\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 9.<br>A square water tank has its side equal to 40 m. There are four semi-circular grassy plots all around it. Find the cost of turfing the plot at? 1.25 per square meter (Take \u03c0 = 3.14).<br>Solution:<br>Side of square tank (a) = 40 m<br>The radius of each semicircular grassy plot = 402 = 20<br><img src=\"https:\/\/farm5.staticflickr.com\/4833\/43860742630_9b9ee504f5_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 15 Areas related to Circles\" width=\"326\" height=\"442\"><\/p>\n<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Question 10.<br>A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all around. Find the cost of leveling the semi-circular flower beds at 60 paise per square meter. (Use \u03c0 = 3.14).<br>Solution:<br>Length of rectangular park (l) = 100 m<br>and width (b) = 50 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4869\/43860742550_a8db40050e_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"253\" height=\"254\"><br>The radius of each semicircular bed along the<br>lengths side (R) =&nbsp;1002 = 50 m<br>and the radius of each semicircular bed along<br>the width side (r) =&nbsp;502&nbsp;= 25 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4876\/43860742480_2b0013c698_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"346\" height=\"353\"><\/p>\n<p>Question 11.<br>The inside perimeter of a running track (shown in the figure) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is anywhere 14 m wide, find the area of the track. Also, find the length of the outer running track.<br><img src=\"https:\/\/farm5.staticflickr.com\/4819\/43860742410_2ac5076aef_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 15 Areas related to Circles\" width=\"328\" height=\"156\"><br>Solution:<br><img src=\"https:\/\/farm2.staticflickr.com\/1946\/43860742350_cbca46fac8_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"373\" height=\"612\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1944\/43860742280_1d8cc2259b_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 15 Areas related to Circles\" width=\"344\" height=\"294\"><\/p>\n<p>Question 12.<br>Find the area of the figure, in square cm, correct to one place of decimal. (Take \u03c0 = 22\/7).<\/p>\n<p><img src=\"https:\/\/farm5.staticflickr.com\/4889\/43860742170_99baed380a_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"297\" height=\"158\"><br>Solution:<br>Join AD<br>ABCD is a square whose each side = 10 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4899\/43860742090_ebf79beb56_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"310\" height=\"161\"><br>Area of square = a\u00b2 = (10)\u00b2 = 100 cm\u00b2<br>Area of half semicircle whose radius is&nbsp;102&nbsp;= 5<br><img src=\"https:\/\/farm5.staticflickr.com\/4806\/43860741960_fe3dbc3c3a_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"209\" height=\"64\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4890\/43860742000_4922b27f58_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"345\" height=\"133\"><\/p>\n<p>Question 13.<br>In the figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as the diameter, a semicircle is added outside the region. Find the area of the shaded region. (Use \u03c0 = 22\/7). [CBSE 2014]<br><img src=\"https:\/\/farm2.staticflickr.com\/1909\/43860741430_56d3b5ff84_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"295\" height=\"161\"><br>Solution:<br>AB = 20 cm, AE = 9 cm, DE = 12 cm<br>\u2220AED = 90\u00b0<br><img src=\"https:\/\/farm5.staticflickr.com\/4853\/43860741820_7644e0fee4_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"347\" height=\"444\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1927\/43860741590_a509255d97_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"279\" height=\"136\"><\/p>\n<p>Question 14.<br>From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of diameter 4.2 cm is also cut from the center as shown in the figure. Find the area of the remaining (shaded) portion of the square. (Use \u03c0 = 22\/7). [CBSE 2010]<\/p>\n<p><img src=\"https:\/\/farm5.staticflickr.com\/4857\/43860741340_051259a4e1_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"195\" height=\"182\"><br>Solution:<br>Side of a square ABCD = 8 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4845\/43860741240_004b754125_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"287\" height=\"357\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4815\/43860741160_5c158c0c30_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles\" width=\"317\" height=\"328\"><\/p>\n<p>Question 15.<br>In the figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC, and AD as diameters, three semi\u00accircles are drawn as shown in the figure. Find the area of the shaded region.<\/p>\n<p><img src=\"https:\/\/farm2.staticflickr.com\/1957\/43860741110_e53321d590_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"270\" height=\"143\"><br>Solution:<br>In the figure, ABCD is a rectangle AB = 14 cm and BC = 7 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1919\/43860741010_cf0a30b229_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles\" width=\"270\" height=\"143\"><br>Two semicircles are drawn on AD and BC as diameter and this semicircle is drawn on Cd as diameter<br>Now area of rectangle ABCD = l x b = 14 x 7 = 98 cm\u00b2<br>Area of two semicircles on AD and BC<br><img src=\"https:\/\/farm5.staticflickr.com\/4884\/43860740910_4c6a64f7b4_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"348\" height=\"491\"><\/p>\n<p>Question 16.<br>In the figure, ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180\u00b0 have been cut off. Calculate :<br>(i) the area of the shaded region.<br>(ii) the length of the boundary of the shaded region.<br><img src=\"https:\/\/farm2.staticflickr.com\/1914\/43860740790_8a3e221619_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"251\" height=\"142\"><br>Solution:<br>ABCD is a rectangle whose Length AB = 20 cm<br>and width BC = 14 cm<br>\u2234 Area of the rectangle = l x b = 20 x 14 = 280 cm\u00b2<br><img src=\"https:\/\/farm5.staticflickr.com\/4803\/43860740870_d60304faf7_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 15 Areas related to Circles\" width=\"365\" height=\"379\"><\/p>\n<p>Question 17.<br>In the figure, the square ABCD is divided into five equal parts, all having the same area. The central part is circular and the lines AE, GC, BF, and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find :<br>(i) the circumference of the central part.<br>(ii) the perimeter of the part ABEF.<br><img src=\"https:\/\/farm5.staticflickr.com\/4864\/43860740660_3950115555_o.png\" alt=\"RD Sharma 10 Chapter 15 Areas related to Circles\" width=\"256\" height=\"204\"><br>Solution:<br>Side of the square ABCD = 22 cm<br>\u2234 Area = (side)\u00b2 = (22)\u00b2 = 484 cm\u00b2<br>\u2235 The square is divided into 5 parts equal in area<br>\u2234 Area of each part =&nbsp;4845&nbsp;cm\u00b2<br><img src=\"https:\/\/farm5.staticflickr.com\/4888\/43860740600_3afef59db6_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 15 Areas related to Circles\" width=\"366\" height=\"691\"><\/p>\n<p>Question 18.<br>In the given figure, Find the area of the shaded region. (Use \u03c0 = 3.14). [CBSE 2015]<br><img src=\"https:\/\/farm5.staticflickr.com\/4878\/43860740540_e8ba20b54d_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"191\" height=\"197\"><br>Solution:<br>Side of large square = 14 cm<br>Radius of each semicircle =&nbsp;42&nbsp;= 2 cm<br>Side of square = 4 cm<br>Area of square = 4 x 4=16 cm\u00b2<br>\u2234 Area of semicircles = 4 x&nbsp;12&nbsp;\u03c0r\u00b2<br>= 2 x 3.14 x 2 x 2<br>= 8 x 3.14<br>= 25.12 cm\u00b2<br>\u2234 Area of shaded region = Area of the large square \u2013 Area of the central portion<br>= (14)2-(16+ 25.12) cm\u00b2<br>= 196-41.12 cm\u00b2<br>= 154.88 .cm\u00b2<\/p>\n<p>Question 19.<br>In the Figure, OACB is a quadrant of a circle with a center of O and a radius 3.5 cm. If OD = 2 cm, find the area of the<br>(i) Quadrant OACB<br>(ii) shaded region.<br><img src=\"https:\/\/farm2.staticflickr.com\/1917\/43860740450_22739f97fc_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"211\" height=\"215\"><br>Solution:<br>The radius of outer quadrant (R) = 3.5 cm<br>and radius of the inner quadrant = 2 cm<br>\u2234 Area of the shaded portion<br>= Area of outer quadrant \u2013 area of inner quadrant<br><img src=\"https:\/\/farm2.staticflickr.com\/1925\/43860740410_752999cfca_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"260\" height=\"115\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4872\/43860740340_224c7234f3_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 15 Areas related to Circles\" width=\"322\" height=\"279\"><\/p>\n<p>Question 20.<br>In the figure, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.[CBSE 2013]<br><img src=\"https:\/\/farm2.staticflickr.com\/1939\/43860740260_4c383b7fa3_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"216\" height=\"201\"><br>Solution:<br>In the figure, OPQ is a quadrant in which<br>OABC is a square OA = 21 cm<br>Join OB,<br><img src=\"https:\/\/farm2.staticflickr.com\/1927\/43860740200_ba635dea67_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 15 Areas related to Circles\" width=\"286\" height=\"242\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4891\/43860740170_182075835d_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"321\" height=\"384\"><\/p>\n<p>Question 21.<br>In the figure, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with center O, then find the area of the shaded region. (Use \u03c0 = 22\/7) [CBSE 2012]<br><img src=\"https:\/\/farm5.staticflickr.com\/4887\/43860740120_6284072b91_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"151\" height=\"143\"><br>Solution:<br>In square OABC, whose side is 7 cm, OAPC<br>is a quadrant<br>Area of square = (side)\u00b2<br>= (7)\u00b2 = 49 cm\u00b2<br>and radius of quadrant = 7 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4838\/43860740060_44c7fd3781_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles\" width=\"360\" height=\"182\"><\/p>\n<p>Question 22.<br>In the figure, OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.<br><img src=\"https:\/\/farm5.staticflickr.com\/4836\/43860739950_01e2e3d67a_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles\" width=\"212\" height=\"203\"><br>Solution:<br>In the figure, OSFT is a quadrant and OEFG<br>is a square inscribed in it<br>The side of the square is OE = 20 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4890\/43860739880_c8749c6a7a_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"347\" height=\"588\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4839\/43860739830_02120000b3_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 15 Areas related to Circles\" width=\"287\" height=\"65\"><\/p>\n<p>Question 23.<br>Find the area of the shaded region in the figure, if AC = 24 cm, BC = 10 cm and O is the center of the circle. (Use \u03c0 = 3.14)<br><img src=\"https:\/\/farm5.staticflickr.com\/4883\/43860739700_9584d62a55_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"268\" height=\"248\"><br>Solution:<br>In right AABC<br>AB\u00b2=AC\u00b2 + BC\u00b2 (Pythagoras Theorem)<br>= (24)\u00b2+ (10)\u00b2<br>= 576 + 100 = 676<br>= (26)\u00b2<br>\u2234 AB = 26 cm<br>\u2234 Diameter of circle = 26 cm<br>and radius (r)=&nbsp;262&nbsp;= 13 cm<br>Now area of the shaded portion<br>= Area of semicircle \u2013 area of right triangle ABC<br><img src=\"https:\/\/farm2.staticflickr.com\/1904\/43860739650_4530531606_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 15 Areas related to Circles\" width=\"307\" height=\"149\"><\/p>\n<p>Question 24.<br>A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (see figure). Find the radius of the inscribed circle and the area of the shaded part.<br><img src=\"https:\/\/farm5.staticflickr.com\/4823\/43860739520_b936357282_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"272\" height=\"213\"><br>Solution:<br>Each side of the equilateral triangle ABC (a) = 12 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4887\/43860739450_c1423b32cb_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"368\" height=\"571\"><\/p>\n<p>Question 25.<br>In the figure, an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take \u03c0 = 3.14)<br><img src=\"https:\/\/farm5.staticflickr.com\/4894\/43860739340_4ae9679c5d_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"237\" height=\"228\"><br>Solution:<br><img src=\"https:\/\/farm5.staticflickr.com\/4870\/43860739260_3f5ddb75dc_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"385\" height=\"709\"><\/p>\n<p>Question 26.<br>A circular field has a perimeter of 650 m. A square plot having its vertices on the circumference of the field is marked in the field. Calculate the area of the square plot.<br>Solution:<br>The perimeter of the circular field = 650 m<br><img src=\"https:\/\/farm2.staticflickr.com\/1912\/43860739120_4dcacce928_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"366\" height=\"430\"><\/p>\n<p>Question 27.<br>Find the area of a shaded region in the figure, where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as the center, (use \u03c0 = 22\/7 and 3\u2013\u221a = 1.73) [CBSE 2015]<br><img src=\"https:\/\/farm2.staticflickr.com\/1937\/43860738860_9fc5c727a7_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"163\" height=\"175\"><br>Solution:<br>The radius of circular arc (r) = 7 cm<br>and side of equilateral AABC (a) = 14 cm and each angle = 60\u00b0<br><img src=\"https:\/\/farm5.staticflickr.com\/4915\/43860739080_02ac22f757_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"185\" height=\"181\"><br>Area of the shaded region<br>=Area of circle + Area of equilateral triangle \u2013 2 area of sector EAF<br><img src=\"https:\/\/farm5.staticflickr.com\/4821\/43860739000_7ca44c270e_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"355\" height=\"291\"><\/p>\n<p>Question 28.<br>A regular hexagon is inscribed in a circle. If the area of the hexagon is 243\u221a cm\u00b2, find the area of the circle. (Use \u03c0 = 3.14) [CBSE 2015]<br>Solution:<br>A regular hexagon ABCDEF is inscribed in a circle<br>Area of hexagon = 24&nbsp;3\u2013\u221a&nbsp;cm\u00b2<br>Let r be the radius of the circle<br>\u2234 Side of regular hexagon = r<br>Area of equilateral \u0394OAB =&nbsp;3\u221a3&nbsp;r\u00b2 sq. units<br><img src=\"https:\/\/farm5.staticflickr.com\/4874\/43860738810_6c0f8127f9_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 15 Areas related to Circles\" width=\"375\" height=\"538\"><\/p>\n<p>Question 29.<br>ABCDEF is a regular hexagon with a center O (see figure). If the area of triangle OAB is 9 cm\u00b2, find the area of :<br>(i) the hexagon and<br>(ii) the circle in which the hexagon is inscribed.<br><img src=\"https:\/\/farm5.staticflickr.com\/4901\/43860738690_dd5ce23fca_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 15 Areas related to Circles\" width=\"182\" height=\"161\"><br>Solution:<br>O is the center of the regular hexagon ABCDEF and the area of the AOAB = 9 cm\u00b2<br>\u2235 By joining the vertices of the hexagon with O,<br>(i) We get 6 equal equilateral triangles<br>\u2234 Area of hexagon = 9 cm\u00b2 x 6 = 54 cm\u00b2<br>(ii) The radius of the circle when this hexagon is inscribed in it will be = OB =AB =r<br><img src=\"https:\/\/farm5.staticflickr.com\/4899\/43860738660_9214e07938_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 15 Areas related to Circles\" width=\"342\" height=\"388\"><\/p>\n<p>Question 30.<br>Four equal circles, each of radius 5 cm, touch each other as shown in the figure. Find the area included between them. (Take \u03c0 = 3.14).<br><img src=\"https:\/\/farm5.staticflickr.com\/4815\/43860738450_eed27ffb20_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles\" width=\"258\" height=\"243\"><br>Solution:<br>The radius of each circle = 5 cm<br>\u2235 The four circles touch each other externally<br>\u2234 By joining their centers, we get a square whose side will be 5 + 5 = 10 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1963\/31806411518_1e5493c328_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 15 Areas related to Circles\" width=\"258\" height=\"237\"><br>Now area of square so formed = a\u00b2 = (10)\u00b2 = 100 cm\u00b2<br>an area of 4 quadrants = 4 x 14 \u03c0r\u00b2= \u03c0r\u00b2<br>= 3.14 x (5)2 cm\u00b2 = 3.14 x 25 cm\u00b2 = 78.5 cm\u00b2<br>\u2234 The area of the part included between the circles<br>= 100 \u2013 78.5<br>= 21.5 cm\u00b2<\/p>\n<p>Question 31.<br>Four equal circles, each of radius \u2018a\u2019 touch each other. Show that the area between them is 67a\u00b2. (Take \u03c0 = 227<br>Solution:<br>Four circles each of radius \u2018a\u2019 touch each other at A, B, C, and D respectively.<br>Their centers are P, Q, R, and S respectively<br>By joining PQ, QR, RS, SD<br><img src=\"https:\/\/farm2.staticflickr.com\/1927\/31806411468_36404c71af_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"267\" height=\"280\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4814\/31806411408_5b0d846edd_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"373\" height=\"298\"><\/p>\n<p>Question 32.<br>A child makes a poster on chart paper drawing a square ABCD of side 14 cm. She draws four circles with center A, B, C, and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles in the given figure. In the shaded region, she write a message \u2018Save Energy\u2019. Find the perimeter and area of the shaded region. (Use \u03c0 = 22\/7) [CBSE 2015]<br><img src=\"https:\/\/farm5.staticflickr.com\/4834\/31806411328_d290e6d67a_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"187\" height=\"172\"><br>Solution:<br>The radius of circular arc (r) = 7 cm<br>Side of square ABCD (a) = 14 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4819\/43860738080_a6064b783e_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"183\" height=\"184\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4864\/31806411098_59b82ce05b_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"343\" height=\"351\"><\/p>\n<p>Question 33.<br>The diameter of a coin is 1 cm (see figure). If four such coins are placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take \u03c0 = 3.1416).<\/p>\n<p><img src=\"https:\/\/farm5.staticflickr.com\/4904\/31806410968_162e2efd27_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"182\" height=\"168\"><br>Solution:<br>The diameter of each coin = 1 cm<br>\u2234 Radius (r) =&nbsp;12&nbsp;cm = 0.5 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1946\/31806410878_3f43d87cbc_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"289\" height=\"229\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1917\/31806410838_cffb4f869f_o.png\" alt=\"Learncbse.In Class 10 Chapter 15 Areas related to Circles\" width=\"372\" height=\"234\"><\/p>\n<p>Question 34.<br>Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of the remaining cardboard. (Use \u03c0 = 22\/7) [CBSE 2013]<br>Solution:<br>Length of rectangle = 14 cm<br>and breadth = 7 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1949\/31806410818_79d591c3d9_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"331\" height=\"435\"><\/p>\n<p>Question 35.<br>In the figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.<br><img src=\"https:\/\/farm5.staticflickr.com\/4844\/31806410668_587c0dfaa7_o.png\" alt=\"Learncbse.In Class 10 Chapter 15 Areas related to Circles\" width=\"249\" height=\"237\"><br>Solution:<br>The radius of larger circle (R) = 7 cm<br>and radius of smaller circle (r) =72&nbsp;cm<br>Area of shaded portion = Area of the larger circle \u2013 an area of the smaller circle<br><img src=\"https:\/\/farm5.staticflickr.com\/4829\/31806410558_582625b857_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"309\" height=\"303\"><\/p>\n<p>Question 36.<br>In the figure, PSR, RTQ, and PAQ are three semi-circles of diameters 10 cm, 3 cm, and 7 cm respectively. Find the perimeter of the shaded region. [CBSE 2014]<br><img src=\"https:\/\/farm2.staticflickr.com\/1935\/31806410478_12e3684eb1_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.4\" width=\"272\" height=\"194\"><br>Solution:<br>Radius of larger semicircle (r<sub>1<\/sub>) =102&nbsp;= 5 cm<br>Radius of large semicircle = (r<sub>2<\/sub>) =&nbsp;72&nbsp;cm<br>Radius of small semicircle (r<sub>3<\/sub>) =&nbsp;32&nbsp;cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1951\/31806410378_1d8d794df3_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"302\" height=\"185\"><\/p>\n<p>Question 37.<br>In the figure, two circles with centers A and B touch each other at point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.<br><img src=\"https:\/\/farm2.staticflickr.com\/1911\/31806410328_42b478d35f_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.4\" width=\"267\" height=\"267\"><br>Solution:<br>In the figure, two circles with centers A and B touch each other internally at C<br>AC = 8 cm and AB = 3 cm<br>\u2234 BC = 8 \u2013 3 = 5 cm<br>\u2234 The radius of the bigger circle (R) = 8 cm<br>and of smaller circle (r) = 5 cm<br>\u2234 Area of shaded portion =Area of a bigger circle \u2013 area of the smaller circle<br><img src=\"https:\/\/farm5.staticflickr.com\/4869\/31806410268_43f3c7ecc8_o.png\" alt=\"Areas related to Circles Class 10 RD Sharma\" width=\"345\" height=\"166\"><\/p>\n<p>Question 38.<br>In the figure, ABCD is a square of side 2a. Find the ratio between<br>(i) the circumferences<br>(ii) the areas of the incircle and the circum- circle of the square.<br><img src=\"https:\/\/farm5.staticflickr.com\/4871\/31806410248_f396eea15c_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles\" width=\"260\" height=\"257\"><br>Solution:<br>A square ABCD is inscribed on a circle<br>The side of the square = 2a<br>and one circle is inscribed in the square ABCD<br>Now diameter of the outer circle is AC<br><img src=\"https:\/\/farm5.staticflickr.com\/4821\/31806410168_6976b605d1_o.png\" alt=\"Areas related to Circles Class 10 RD Sharma\" width=\"366\" height=\"297\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1942\/31806410108_001afd9bb5_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles\" width=\"383\" height=\"267\"><\/p>\n<p>Question 39.<br>In the figure, there are three semicircles, A, B, and C having a diameter of 3 cm each, and another semicircle E having a circle of D with a diameter of 4.5 cm. Calculate :<br>(i) the area of the shaded region<br>(ii) the cost of painting the shaded region at the rate of 25 paise per cm\u00b2, to the nearest rupee.<\/p>\n<p><img src=\"https:\/\/farm5.staticflickr.com\/4832\/31806410058_81783d1ffb_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.4\" width=\"330\" height=\"241\"><br>Solution:<br><img src=\"https:\/\/farm5.staticflickr.com\/4822\/31806409948_c218fa0fde_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"390\" height=\"237\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4871\/31806410018_ca16da6c24_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"382\" height=\"622\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4844\/31806409878_6c62ec0420_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"359\" height=\"280\"><\/p>\n<p>Question 40.<br>In the figure, ABC is a right-angled triangle, \u2220B = 90\u00b0, AB = 28 cm and BC = 21 cm. With AC as diameter, a semicircle is drawn and with BC as radius, a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.<br><img src=\"https:\/\/farm5.staticflickr.com\/4889\/31806409748_20e4031768_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 15 Areas related to Circles\" width=\"216\" height=\"216\"><br>Solution:<br>In the right \u0394ABC,<br>AB = 28 cm, BC = 21 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4867\/31806409728_f11d675628_o.png\" alt=\"Learncbse.In Class 10 Chapter 15 Areas related to Circles\" width=\"362\" height=\"616\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1954\/31806409628_409416aaee_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 15 Areas related to Circles\" width=\"359\" height=\"303\"><\/p>\n<p>Question 41.<br>In the figure, O is the center of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take \u03c0 = 3.142)<br><img src=\"https:\/\/farm5.staticflickr.com\/4911\/44953853464_4fea5a48a0_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"325\" height=\"175\"><br>Solution:<br>A semicircle is drawn on the diameter AB<br>\u0394ACB is drawn in this semicircle in right \u0394ACB<br>AC = 12 cm and BC = 16 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4859\/44953853394_b31ac0dc6f_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 15 Areas related to Circles\" width=\"358\" height=\"268\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1932\/30738147927_d34f25d8dc_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"331\" height=\"339\"><\/p>\n<p>Question 42.<br>In the figure, the boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find<br>(i) the length of the boundary,<br>(ii) the area of the shaded region.<br><img src=\"https:\/\/farm5.staticflickr.com\/4803\/30738147857_856e8c6e24_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"348\" height=\"238\"><br>Solution:<br>Diameter of the biggest semicircle = 14 cm 14<br>\u2234 Radius (R) =&nbsp;142&nbsp;= 7 cm<br>Diameter of the small semicircle = 7 cm 7<br>\u2234 Radius (r<sub>1<\/sub>) =&nbsp;72&nbsp;cm<br>and diameter of each smaller circle = 3.5 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1976\/30738147777_4d60826481_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"377\" height=\"712\"><\/p>\n<p>Question 43.<br>In the figure, AB = 36 cm and M is the mid\u00acpoint of AB. Semi-circles are drawn on AB, AM, and MB as diameters. A circle with center C touches all three circles. Find the area of the shaded region.<br><img src=\"https:\/\/farm2.staticflickr.com\/1922\/30738147657_63ed58aac4_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"305\" height=\"159\"><br>Solution:<br>In the figure, there are three semicircles one bigger and two smaller There is one small circle that also<br>Now diameter of the bigger semicircle = is 36 cm<br>\u2234 Radius (R) =&nbsp;362&nbsp;= 18 cm<br>and diameter of each smaller semicircle = 18 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1967\/30738147567_ed32f93bd4_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"365\" height=\"773\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4808\/30738147457_0cecb5ba47_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"337\" height=\"94\"><\/p>\n<p>Question 44.<br>In the figure, ABC is a right-angled triangle in which \u2220A = 90\u00b0, AB = 21 cm and AC = 28 cm. Semi-circles are described on AB, BC, and AC as diameters. Find the area of the shaded region.<br><img src=\"https:\/\/farm5.staticflickr.com\/4854\/44953852884_d5025db14e_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"279\" height=\"164\"><br>Solution:<br>In the figure, ABC is a right triangle in a semicircle \u2220A = 90\u00b0, AB = 21 cm, and AC = 28 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1967\/44953852804_45633061bc_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"304\" height=\"183\"><br>Semi-circles are drawn on BC and AC as diameters<br>In right \u0394ABC<br>BC\u00b2 = AB\u00b2+AC\u00b2 (Pythagoras Theorem)<br>= 21\u00b2+ 28\u00b2<br>= 441 + 784= 1225 = (35)\u00b2<br>\u2234 BC = 35 cm<br>Now the radius of the bigger semicircle (R) = 352 cm,<br>of semicircle at AB =&nbsp;212&nbsp;cm and of<br>semicircle on AC =&nbsp;282&nbsp;cm = 14 cm<br>Now area of the shaded portion<br>= Area of semicircle on AB as diameter + area of semicircle on AC as diameter + area of \u0394ABC \u2013 area of semicircle on BC as diameter<br><img src=\"https:\/\/farm2.staticflickr.com\/1909\/44953852724_af7c50e242_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"363\" height=\"500\"><\/p>\n<p>Question 45.<br>In the figure, shows the cross-section of a railway tunnel. The radius OA of the circular part is 2 m. If \u2220AOB = 90\u00b0, calculate :<br>(i) the height of the tunnel<br>(ii) the perimeter of the cross-section<br>(iii) the area of the cross-section.<br><img src=\"https:\/\/farm5.staticflickr.com\/4912\/44953852644_b4b1b8f48f_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"159\" height=\"150\"><br>Solution:<br>The radius of the circular part of the tunnel = 2 m<br>i.e. OA = OB = 2 m<br>and \u2220AOB = 90\u00b0<br>OD \u22a5 AB<br>\u2234 D in mid-point of AB<br>\u2234 In right \u0394AOB,<br><img src=\"https:\/\/farm5.staticflickr.com\/4833\/30738146907_6ccc08c4ba_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"350\" height=\"576\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4886\/45628063342_7b1c70e5c0_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"381\" height=\"270\"><\/p>\n<p>Question 46.<br>In the figure, shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and \u0394CEF is an isosceles right-angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.<br><img src=\"https:\/\/farm2.staticflickr.com\/1978\/30738146727_d0e97cb3fe_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles \" width=\"259\" height=\"237\"><br>Solution:<br>ABCD is a square with side = 42 cm<br>BCD is a quadrant in which \u2220BCD = 90\u00b0 and radius = 42 cm<br>\u0394CEF is an isosceles right triangle in which CE = CF = 6 cm<br><img src=\"https:\/\/farm2.staticflickr.com\/1931\/30738146617_58d3dd73ae_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles \" width=\"356\" height=\"452\"><\/p>\n<p>Question 47.<br>In the figure, ABCD is a trapezium of area 24.5 cm2. In it, AD || BC, \u2220DAB = 90\u00b0, AD = 10 cm, and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. (Take \u03c0 \u2013 (22\/7). [ cbse2014]<br><img src=\"https:\/\/farm5.staticflickr.com\/4855\/45628063272_39195e1132_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles \" width=\"310\" height=\"193\"><br>Solution:<br>In the figure, ABCD is a trapezium<br>Area = 24.5 cm2, AD || BC<br>\u2220DAB = 90\u00b0, AD = 10 cm BC = 4 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4905\/30738146387_430820fe01_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles\" width=\"316\" height=\"485\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4911\/30738146197_b9b5a8f55d_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"333\" height=\"225\"><\/p>\n<p>Question 48.<br>In the figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm, and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centers A, B, C, and D have been drawn. Then, find the area of the shaded region of the figure. (Use \u03c0 = 22\/7). [CBSE 2014]<br><img src=\"https:\/\/farm2.staticflickr.com\/1946\/30738146087_323e93d755_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 15 Areas related to Circles\" width=\"271\" height=\"129\"><br>Solution:<br>In trapezium ABCD<br>AB || DC<br>AB = 18 cm, DC = 32 cm Height = 14 cm<br>Radius of each at the corner of trapezium = 7 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4823\/30738145957_d6f6ac74d2_o.png\" alt=\"RD Sharma 10 Chapter 15 Areas related to Circles\" width=\"323\" height=\"249\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4818\/30738145847_3719ae4e7f_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 15 Areas related to Circles\" width=\"243\" height=\"295\"><\/p>\n<p>Question 49.<br>From a thin metallic piece, in the shape of a trapezium ABCD, in which AB || CD and \u2220BCD = 90\u00b0, a quarter circle BEFC is removed (see figure). Given AB = BC = 3.5 cm and DE = 2 cm, calculate the area of the remaining piece of the metal sheet.<br><img src=\"https:\/\/farm5.staticflickr.com\/4893\/30738145447_ebfc8f15ac_o.png\" alt=\"RD Sharma 10 Chapter 15 Areas related to Circles\" width=\"341\" height=\"242\"><br>Solution:<br>ABCD is a trapezium in shape in which<br>AB || CD and \u2220BCD = 90\u00b0<br>AB = BC = 3.5 cm, DE = 2 cm<br>\u2234 DC = DE + EC = DE + BC = 2 + 3.5 = 5.5 cm<br>Now area of trapezium ABCD =&nbsp;12&nbsp;(AB + CD) x BC (\u2235 BC is height)<br><img src=\"https:\/\/farm5.staticflickr.com\/4809\/30738145717_67a000250b_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"237\" height=\"58\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1951\/30738145507_01a5d39fc5_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"371\" height=\"287\"><\/p>\n<p>Question 50.<br>In the figure, ABC is an equilateral triangle of side 8 cm. A, B, and C are the centers of circular arcs of radius 4 cm. Find the area of the shaded region correct up to 2 decimal places. (Take \u03c0 = 3.142<br>and&nbsp;3\u2013\u221a = 1.732).<br><img src=\"https:\/\/farm2.staticflickr.com\/1961\/30738145287_e58876fcfa_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 15 Areas related to Circles\" width=\"182\" height=\"158\"><br>Solution:<br>In the figure, ABC is an equilateral triangle with 8 cm as a side with centers A, B, and C,<br>circular arcs drawn of radius 4 cm<br>Each side of \u0394ABC = 8 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4829\/30738145197_1bcfb49aeb_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"255\" height=\"241\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1948\/30738145037_8190cf1dde_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 15 Areas related to Circles\" width=\"303\" height=\"349\"><\/p>\n<p>Question 51.<br>The sides of a triangular field are 15 m, 16 m, and 17 m. With the three corners of the field a cow, a buffalo, and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals. (NCERT Exemplar)<br>Solution:<br>Given that, a triangular field with the three comers of the field a cow, a buffalo, and a horse are tied separately with ropes. So, each animal grazed the field in each corner of the triangular field as a sectorial form.<br>Given, the radius of each sector (r) = 7m<br><img src=\"https:\/\/farm5.staticflickr.com\/4907\/30738144827_b60203d6b0_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles\" width=\"263\" height=\"270\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4845\/30738144247_1b17364375_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"399\" height=\"115\"><br><img src=\"https:\/\/farm2.staticflickr.com\/1948\/43860744170_bf48c7132a_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles\" width=\"357\" height=\"642\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4879\/43860744230_c5c6d7b2ff_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"359\" height=\"353\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4912\/43860744290_effdcf96ce_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 15 Areas related to Circles\" width=\"344\" height=\"61\"><\/p>\n<p>Question 52.<br>In the given figure, the side of a square is 28 cm, and the radius of each circle is half of the length of the side of the square where O and O\u2019 are the centers of the circles. Find the area of the shaded region. [CBSE 2017]<br><img src=\"https:\/\/farm2.staticflickr.com\/1923\/30738158767_412a547427_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"269\" height=\"260\"><br>Solution:<br><img src=\"https:\/\/farm2.staticflickr.com\/1923\/43860744070_35c6f86399_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 15 Areas related to Circles\" width=\"377\" height=\"371\"><\/p>\n<p>Question 53.<br>In a hospital, water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park to a hospital whose length is 25 m and breadth is 20 m. If the tank is filled completely then what will be the height of standing water used for irrigating the park? [CBSE 2017]<br>Solution:<br>Diameter of cylinder (d) = 2 m<br>The radius of cylinder (r) = 1 m<br>Height of cylinder (H) = 5 m<br>Volume of cylindrical tank, Vc = = \u03c0r\u00b2H = \u03c0 X (1) 2 X 5= 5\u03c0m<br>Length of the park (L) = 25 m<br>Now water from the tank is used to irrigate the park. So, the volume of the cylindrical tank = Volume of water in the park.<br>\u21d2 5\u03c0 = 25 x 20 x h<br>\u21d2 5\u03c0\/25 x 20 = h<br>\u21d2 h = \u03c0\/100 m<br>\u21d2 h = 0.0314 m<br>Through the recycling of water, better use of the natural resource occurs without wastage. It helps in reducing and preventing pollution.<br>It thus helps in conserving water. This keeps the greenery alive in urban areas like in parks gardens etc.<\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>&nbsp;Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-15-exercise-154\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631787094572\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-get-rd-sharma-class-10-solutions-chapter-15-exercise-154-free-pdf\"><\/span>Where can I get RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can get RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631787193738\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"why-should-one-choose-rd-sharma-class-10-solutions-chapter-15-exercise-154-from-kopykitab\"><\/span>Why should one choose RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 from Kopykitab?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Kopykitab\u2019s experts provide 100 percent appropriate solutions so that students can succeed in their board exams. After performing extensive research on each concept, a team of subject expert tutors formulates the solutions. Students who have doubts about how to answer textbook questions can check the chapter solutions to obtain a better understanding of the overall topics.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631787264946\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-the-rd-sharma-class-10-solutions-chapter-15-exercise-154-available-on-the-kopykitab-website\"><\/span>Is the RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 available on the Kopykitab website?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, the PDFs of RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4 are available. These solutions are created in a unique method by Kopykitab\u2019s expert faculty.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.4:&nbsp;This exercise includes problems involving calculating the area of such plane figure combinations. Students can use the RD Sharma Class 10 Solutions provided by experts at Kopykitab to get complete solutions to all exercise problems. Students can also download the RD Sharma Solutions for Class 10 Maths &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.4 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-15-exercise-15-4\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.4 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":128447,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128435"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=128435"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128435\/revisions"}],"predecessor-version":[{"id":510071,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128435\/revisions\/510071"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/128447"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=128435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=128435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=128435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}