{"id":128433,"date":"2021-09-16T15:56:33","date_gmt":"2021-09-16T10:26:33","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=128433"},"modified":"2023-12-01T10:49:35","modified_gmt":"2023-12-01T05:19:35","slug":"rd-sharma-class-10-solutions-chapter-15-exercise-15-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-15-exercise-15-1\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.1 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-128444\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.1.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-15-Exercise-15.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1:&nbsp;<\/strong>The perimeter and area of a circle, as well as the area contained by two concentric circles, are all problems in this exercise. 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> to find thorough solutions to problems and to clear their doubts. 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 15.1 PDF is available for download below.<\/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-69d4aab87b9c3\" 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 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id=\"download-rd-sharma-class-10-solutions-chapter-15-exercise-151-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1 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-15.1.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-15.1.pdf\">RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1<\/a><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-15-exercise-151-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 15 Exercise 15.1- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br>Find the circumference and area of a circle of radius 4.2 cm.<br>Solution:<br>Radius of a circle = 4.2 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4832\/46282465261_878e1e647e_o.png\" alt=\"RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"336\" height=\"206\"><\/p>\n<p>Question 2.<br>Find the circumference of a circle whose area is 301.84 cm<sup>2<\/sup>.<br>Solution:<br>Area of a circle = 301.84 cm<sup>2<br><\/sup>Let r be the radius, then \u03c0r<sup>2<\/sup>&nbsp;= 301.84<br><img src=\"https:\/\/farm5.staticflickr.com\/4859\/46282465181_78a92687bc_o.png\" alt=\"Areas related to Circles Class 10 RD Sharma\" width=\"305\" height=\"186\"><\/p>\n<p>Question 3.<br>Find the area of a circle whose circum\u00adference is 44 cm.<br>Solution:<br>Circumference of a circle = 44 cm<br>Let r be the radius,<br>then 2\u03c0r = circumference<br><img src=\"https:\/\/farm5.staticflickr.com\/4877\/46282465001_8bdfcebb2d_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles\" width=\"311\" height=\"163\"><\/p>\n<p>Question 4.<br>The circumference of a circle exceeds the diameter by 16.8 cm. Find the circum\u00adference of the circle. (C.B.S.E. 1996)<br>Solution:<br>Let r be the radius of the circle<br>\u2234 Circumference = 2r + 16.8 cm<br>\u21d2 2\u03c0r = 2r + 16.8<br>\u21d2 2\u03c0r \u2013 2r = 16.8<br><img src=\"https:\/\/farm5.staticflickr.com\/4853\/46282464901_b0f7ed52cf_o.png\" alt=\"RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.1\" width=\"342\" height=\"250\"><\/p>\n<p>Question 5.<br>A horse is tied to a pole with 28 m long string. Find the area where the horse can graze. (Take \u03c0 = 22\/7)<br>Solution:<br>Radius of the circle (r) = Length of the rope = 28 m .<br>Area of the place where the horse can graze<br><img src=\"https:\/\/farm5.staticflickr.com\/4819\/46282464861_c095a88e73_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"237\" height=\"104\"><\/p>\n<p>Question 6.<br>A steel wire when bent in the form of a square encloses an area of 121 cm<sup>2<\/sup>. If the same wire is bent in the form of a circle, find the area of the circle. (C.B.S.E. 1997)<br>Solution:<br>Area of square formed by a wire =121 cm<sup>2<br><\/sup>\u2234 Side of square (a) =&nbsp;Area\u2212\u2212\u2212\u2212\u221a =&nbsp;121\u2212\u2212\u2212\u221a = 11 cm Perimeter of the square = 4 x side = 4 x 11 = 44 cm<br>\u2234Circumference of the circle formed by the wire = 44cm<br>Let r be the radius<br><img src=\"https:\/\/farm5.staticflickr.com\/4859\/46282464791_35c9aaee67_o.png\" alt=\"RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"257\" height=\"252\"><\/p>\n<p>Question 7.<br>The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.<br>Solution:<br>Let R and r be the radii of two circles and their ratio between them circumference = 2 : 3<br><img src=\"https:\/\/farm5.staticflickr.com\/4842\/46282464751_cbe992be4a_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"257\" height=\"215\"><\/p>\n<p>Question 8.<br>The sum of radii of two circles is 140 cm and the difference of their circum\u00adferences is 88 cm. Find the diameters of the circles.<br>Solution:<br>Let R and r be the radii of two circles Then R + r = 140 cm \u2026\u2026.(i)<br>and difference of their circumferences<br><img src=\"https:\/\/farm5.staticflickr.com\/4918\/46282464671_db00880b03_o.png\" alt=\"RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles\" width=\"179\" height=\"112\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4808\/46282464621_5014e38825_o.png\" alt=\"RD Sharma Solutions Class 10 Chapter 15 Areas related to Circles\" width=\"345\" height=\"271\"><\/p>\n<p>Question 9.<br>Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm. [NCERT Exemplar]<br>Solution:<br>Let the radius of a circle be r.<br>Circumference of a circle = 2\u03c0r<br>Let the radii of two circles are r<sub>1<\/sub>&nbsp;and r<sub>2<\/sub>&nbsp;whose<br>values are 15 cm and 18 cm respectively.<br>i.e., r<sub>1<\/sub>&nbsp;= 15 cm and r<sub>2<\/sub>&nbsp;= 18 cm<br>Now, by given condition,<br>Circumference of circle = Circumference of first circle + Circumference of second circle<br>\u21d2 2\u03c0r = 2\u03c0 r<sub>1<\/sub>&nbsp;+ 2\u03c0r<sub>2&nbsp;<\/sub>=<br>\u21d2 r = r<sub>1<\/sub>&nbsp;+ r<sub>2<br><\/sub>\u21d2 r = 15 + 18<br>\u2234 r = 33 cm<br>Hence, required radius of a circle is 33 cm.<\/p>\n<p>Question 10.<br>The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.<br>Solution:<br>Radius of first circle (r<sub>1<\/sub>) = 8 cm<br>and radius of second circle (r<sub>2<\/sub>) = 6 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4823\/46282464531_00736398da_o.png\" alt=\"Learncbse.In Class 10 Chapter 15 Areas related to Circles\" width=\"342\" height=\"117\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4916\/46282464441_b7e0cc2861_o.png\" alt=\"Class 10 RD Sharma Solutions Chapter 15 Areas related to Circles\" width=\"304\" height=\"97\"><\/p>\n<p>Question 11.<br>The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.<br>Solution:<br>Radius of the first circle (r<sub>1<\/sub>) = 19 cm<br>and radius of the second circle (r<sub>2<\/sub>) = 9 cm S<br>um of their circumferences = 2\u03c0r<sub>1<\/sub>&nbsp;+ 2\u03c0r<sub>2<br><\/sub>= 2\u03c0 (r<sub>1&nbsp;<\/sub>+ r<sub>2<\/sub>) = 2\u03c0 (19 + 9) cm<br>= 2\u03c0 x 28 = 56\u03c0 cm<br>Let R be the radius of the circle whose circumference is the sum of the circum\u00adferences of given two circles, then<br><img src=\"https:\/\/farm5.staticflickr.com\/4809\/46282464501_5dbcc6a65d_o.png\" alt=\"RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles \" width=\"305\" height=\"181\"><\/p>\n<p>Question 12.<br>The area of a circular playground is 22176 m<sup>2<\/sup>. Find the cost of fencing this ground at the rate of \u20b950 per metre. [NCERT Exempiar]<br>Solution:<br>Given, area of a circular playground = 22176 m<sup>2<\/sup><br><img src=\"https:\/\/farm5.staticflickr.com\/4857\/46282464331_fc2a7af8c8_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 15 Areas related to Circles\" width=\"343\" height=\"218\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4905\/46282464281_3d00467a9e_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"315\" height=\"46\"><\/p>\n<p>Question 13.<br>The side of a square is 10 cm. Find the area of circumscribed and inscribed circles.<br>Solution:<br>ABCD is a square whose each side is 10 cm<br>\u2234 AB = BC = CD = DA = 10 cm<br>AC and BD are its diagonals<br><img src=\"https:\/\/farm5.staticflickr.com\/4843\/46282464221_d83608cd07_o.png\" alt=\"RD Sharma Class 10 Solution Chapter 15 Areas related to Circles\" width=\"186\" height=\"174\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4840\/44465649880_c474d8da6b_o.png\" alt=\"RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles\" width=\"348\" height=\"566\"><\/p>\n<p>Question 14.<br>If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.<br>Solution:<br>Let r be the radius of the circle a be the side of the square<br><img src=\"https:\/\/farm5.staticflickr.com\/4849\/44465649740_3f4bb2f547_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"219\" height=\"210\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4918\/46282463961_2eb4ed1be1_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"343\" height=\"619\"><\/p>\n<p>Question 15.<br>The area of a circle inscribed in an equilateral triangle is 154 cm<sup>2<\/sup>. Find the perimeter of the triangle.&nbsp;(Use \u03c0 = 22\/7 and&nbsp;3\u2013\u221a = 1.73)<br>Solution:<br>Area of the inscribed circle of \u0394ABC = 154 cm<sup>2<\/sup><br><img src=\"https:\/\/farm5.staticflickr.com\/4867\/44465649540_393d848b65_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"265\" height=\"241\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4815\/46282463821_58049d7ebe_o.png\" alt=\"RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles\" width=\"331\" height=\"481\"><\/p>\n<p>Question 16.<br>A field is in the form of a circle. A fence is to be erected around the field. The cost of fencing would be \u20b92640 at the rate of \u20b912 per metre. Then, the field is to be thoroughly ploughed at the cost of \u20b90.50 per m<sup>2<\/sup>. What is the amount required to plough the field ? (Take \u03c0&nbsp;= 22\/7)<br>Solution:<br>Cost of the fencing the circular field = \u20b92640<br>Rate = \u20b912 per metre 2640<br>\u2234 Circumference =&nbsp;(264012)&nbsp;= 220 m<br>Let r be the radius of the field, then = 2\u03c0r = 220<br><img src=\"https:\/\/farm5.staticflickr.com\/4843\/46282463451_21b6c659ed_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"334\" height=\"270\"><\/p>\n<p>Question 17.<br>A park is in the form of a rectangle 120 m x 100 m. At the centre of the park there is a circular lawn. The area of park excluding lawn is 8700 m<sup>2<\/sup>. Find the radius of the circular lawn. (Use \u03c0 = 22\/7).<br>Solution:<br>Area of the park excluding lawn = 8700 m<sup>2<br><\/sup>Length of rectangular park = 120 m<br>and width = 100 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4890\/46282463411_7cb678f193_o.png\" alt=\"Class 10 RD Sharma Chapter 15 Areas related to Circles\" width=\"233\" height=\"166\"><br>\u2234 Area of lawn = l x b<br>= 120 x 100 m<sup>2<\/sup>&nbsp;= 12000 m<sup>2<br><\/sup>Let r be the radius of the circular lawn, then area of lawn = \u03c0r<sup>2<\/sup><br><img src=\"https:\/\/farm5.staticflickr.com\/4881\/46282463291_2052ceeb1a_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"276\" height=\"145\"><\/p>\n<p>Question 18.<br>A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of the its wheels.<br>Solution:<br>Distance covered by the car in 450 revolutions = 1 km = 1000 m<br>\u2234 Distance covered in 1 revolution =&nbsp;(1000450)<br>=&nbsp;(209)&nbsp;m<br><img src=\"https:\/\/farm5.staticflickr.com\/4811\/46282463191_1f0d6e73fa_o.png\" alt=\"RD Sharma Maths Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"342\" height=\"257\"><\/p>\n<p>Question 19.<br>The area of enclosed between the concentric circles is 770 cm<sup>2<\/sup>. If the radius of the outer circle is 21 cm, find the radius of the inner circle.<br>Solution:<br>Area of enclosed between two concentric circles = 770 cm<sup>2<br><\/sup>Radius of the outer circle (R) = 21 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4833\/46282463161_e187509d6f_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"335\" height=\"589\"><\/p>\n<p>Question 20.<br>An archery target has three regions formed by the concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.[NCERT Exemplar]<br><img src=\"https:\/\/farm5.staticflickr.com\/4871\/46282462921_5f215afc3f_o.png\" alt=\"RD Sharma 10 Class Solutions Chapter 15 Areas related to Circles\" width=\"151\" height=\"143\"><br>Solution:<br>Let the diameters of concentric circles be k, 2k , 3k<br><img src=\"https:\/\/farm5.staticflickr.com\/4851\/45558940274_2540eff721_o.png\" alt=\"RD Sharma Class 10 Textbook PDF Chapter 15 Areas related to Circles\" width=\"349\" height=\"525\"><\/p>\n<p>Question 21.<br>The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km\/hr? [NCERT Exemplar]<br>Solution:<br>Given, radius of wheel, r = 35 cm<br>Circumference of the wheel = 2\u03c0r<br>= 2 x&nbsp;(227)&nbsp;x 35 = 220 cm<br>But speed of the wheel = 66 kmh<sup>-1<br><\/sup>=&nbsp;(66&#215;100060)&nbsp;m\/ mm<br>= 1100 x 100 cm min<sup>-1<br><\/sup>= 110000 cm min<sup>-1<\/sup><sup><br><\/sup>\u2234 Number of revolutions in 1 min<br>=&nbsp;(110000220)= 500 revolution<br>Hence, required number of revolutions per minute is 500.<\/p>\n<p>Question 22.<br>A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of \u20b925 per m<sup>2<\/sup>. [NCERT Exemplar]<br>Solution:<br>Given that, a circular pond is surrounded by a wide path.<br>The diameter of circular pond = 17.5 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4862\/45558940174_0cfdede80d_o.png\" alt=\"Maths RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles\" width=\"345\" height=\"697\"><\/p>\n<p>Question 23.<br>A circular park is surrounded by a rod 21 m wide. If the radius of the park is 105 m, find the area of the road. [NCERT Exemplar]<br>Solution:<br>Given that, a circular park is surrounded by a road.<br>Width of the road = 21 m<br>Radius of the park (r<sub>1<\/sub>) = 105 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4918\/45558940074_72015c52e9_o.png\" alt=\"10th Maths Solution Book Pdf Chapter 15 Areas related to Circles\" width=\"243\" height=\"144\"><br>.\u2019. Radius of whole circular portion (park + road),<br>r<sub>e<\/sub>&nbsp;= 105 + 21 = 126 m<br>Now, area of road = Area of whole circular portion \u2013 Area of circular park<br>= \u03c0r<sup>2<\/sup>&nbsp;\u2013 \u03c0r<sup>2<\/sup> [\u2235 area of circle = \u03c0r<sup>2<\/sup>]<br><img src=\"https:\/\/farm5.staticflickr.com\/4883\/45558940014_683a935f6e_o.png\" alt=\"RD Sharma 10 Chapter 15 Areas related to Circles\" width=\"325\" height=\"269\"><\/p>\n<p>Question 24.<br>A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square. [NCERT Exemplar]<br>Solution:<br>Let the side of a square be a and the radius of circle be r.<br>Given that, length of diagonal of square = 8 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4876\/45558939844_dfce9aa91e_o.png\" alt=\"RD Sharma Class 10 Book Pdf Chapter 15 Areas related to Circles\" width=\"351\" height=\"501\"><\/p>\n<p>Question 25.<br>A path of 4 m width runs round a semi\u00adcircular grassy plot whose circumference is 81&nbsp;(57)m. Find:<br>(i) the area of the path<br>(ii) the cost of gravelling the path at the rate of \u20b91.50 per square metre<br>(iii) the cost of turfing the plot at the rate of 45 paise per m<sup>2<\/sup>.<br>Solution:<br>Width of path around the semicircular grassy plot = 4 m<br>Circumference of the plot = 81&nbsp;(57)m<br>=&nbsp;(5727)&nbsp;m<br>Let r be the radius of the plot, then<br><img src=\"https:\/\/farm5.staticflickr.com\/4811\/45558939514_3f0a1b3b01_o.png\" alt=\"Solution Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"322\" height=\"79\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4879\/46282462411_bf599e1549_o.png\" alt=\"RD Sharma 10 Solutions Chapter 15 Areas related to Circles\" width=\"364\" height=\"848\"><\/p>\n<p>Question 26.<br>Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.<br>Solution:<br>Radius of first circle (r<sub>1<\/sub>) = 3.5 cm<br>Radius of second circle (r<sub>2<\/sub>) = 7 cm<br><img src=\"https:\/\/farm5.staticflickr.com\/4810\/46282462221_e0b3d6d790_o.png\" alt=\"RD Sharma Maths Book For Class 10 Solution Chapter 15 Areas related to Circles\" width=\"355\" height=\"823\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4904\/45558939264_0f15e61cba_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"333\" height=\"118\"><\/p>\n<p>Question 27.<br>A path of width 3.5 m runs around a semi\u00adcircular grassy plot whose perimeter is 72 m. Find the area of the path. (Use \u03c0 = 22\/7) [CBSE 2015]<br>Solution:<br>Perimeter of semicircle grassy plot = 72 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4870\/45558939064_c747bd7bb5_o.png\" alt=\"RD Sharma Mathematics Class 10 Pdf Download Free Chapter 15 Areas related to Circles\" width=\"219\" height=\"132\"><br>Let r be the radius of the plot<br><img src=\"https:\/\/farm5.staticflickr.com\/4828\/45558938954_62d50a8a09_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"349\" height=\"536\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4885\/45558938764_048d1d6ddb_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"116\" height=\"35\"><\/p>\n<p>Question 28.<br>A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of \u20b925 per square metre (Use \u03c0 = 3.14) [CBSE 2014]<br>Solution:<br>Diameter of circular pond (d) = 17.5 m<br>Radius (r) =(17252)&nbsp;= 8.75 m<br>Width of path = 2m<br>\u2234 Radius of outer cirlce (R) = 8.75 + 2 = 10.75 m<br>Area of path = (R<sup>2<\/sup>&nbsp;\u2013 r<sup>2<\/sup>)\u03c0<br>= [(10.75)<sup>2<\/sup>&nbsp;\u2013 (8.75)<sup>2<\/sup>](3.14)<br>= 3.14(10.75 + 8.75) (10.75 \u2013 8.75)<br>= 3.14 x 19.5 x 2 = 122.46 m<sup>2<br><\/sup>Cost of 1 m<sup>2<\/sup>&nbsp;for constructing the path \u20b925 m<sup>2<br><\/sup>\u2234 Total cost =&nbsp;\u20b9 122.46 x 25 = \u20b93061.50<\/p>\n<p>Question 29.<br>The outer circumference of a circular race-track is 528 m. The track is every\u00adwhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre (Use \u03c0= 22\/7).<br>Solution:<br>Let R and r be the radii of the outer and inner of track.<br>Outer circumference of the race track = 528 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4821\/45558938734_6fa3b85d79_o.png\" alt=\"Class 10 RD Sharma Pdf Chapter 15 Areas related to Circles\" width=\"290\" height=\"334\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4825\/45558938654_282fc27215_o.png\" alt=\"RD Sharma Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles\" width=\"336\" height=\"359\"><\/p>\n<p>Question 30.<br>A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road.<br>Solution:<br>Width of the road = 7 m<br><img src=\"https:\/\/farm5.staticflickr.com\/4858\/45558938564_d06af43061_o.png\" alt=\"Answers Of RD Sharma Class 10 Chapter 15 Areas related to Circles\" width=\"197\" height=\"189\"><br>Circumference of the park = 352 m<br>Let r be the radius, then 2\u03c0r = 352<br><img src=\"https:\/\/farm5.staticflickr.com\/4810\/46282461431_ccdbe61dd4_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"297\" height=\"208\"><br><img src=\"https:\/\/farm5.staticflickr.com\/4902\/45558938304_0574e777cc_o.png\" alt=\"RD Sharma Class 10 Maths Chapter 15 Areas related to Circles\" width=\"248\" height=\"111\"><\/p>\n<p>Question 31.<br>Prove that the area of a circular path of uniform width hsurrounding a circular region of radius r is \u03c0h(2r + h).<br>Solution:<br>Radius of inner circle = r<br>Width of path = h<br>\u2234 Outer radius (R) = (r + h)<br>\u2234 Area of path = \u03c0R<sup>2<\/sup>&nbsp;\u2013 \u03c0r<sup>2<br><\/sup>= \u03c0 {(r + h)<sup>2<\/sup>&nbsp;\u2013 r<sup>2<\/sup>}<br>= \u03c0 {r<sup>2<\/sup>&nbsp;+ h<sup>2<\/sup>&nbsp;+ 2rh \u2013 r<sup>2<\/sup>}<br>= \u03c0 {2rh + h<sup>2<\/sup>}<br>= \u03c0h (2r + h) Hence proved.<\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1. 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-151\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1<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-1631787073820\" 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-151-free-pdf\"><\/span>Where can I get RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1 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 15.1 Free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631787175066\" 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-151-from-kopykitab\"><\/span>Why should one choose RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1 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-1631787251359\" 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-151-available-on-the-kopykitab-website\"><\/span>Is the RD Sharma Class 10 Solutions Chapter 15 Exercise 15.1 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 15.1 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 15.1:&nbsp;The perimeter and area of a circle, as well as the area contained by two concentric circles, are all problems in this exercise. Students can use the RD Sharma Class 10 Solutions to find thorough solutions to problems and to clear their doubts. The RD Sharma Solutions &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.1 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-15-exercise-15-1\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 15 Areas Related to Circles Exercise 15.1 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":128444,"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\/128433"}],"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=128433"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128433\/revisions"}],"predecessor-version":[{"id":515153,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/128433\/revisions\/515153"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/128444"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=128433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=128433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=128433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}