<\/span><\/h2>\nQuestion 1.
In a cylinder, if radius is doubled and height is halved, curved surface area will be
(a) halved
(b) doubled
(c) same
(d) four times
Solution:
Let radius of the first cylinder (r1<\/sub>) = r
and height (h1<\/sub>) = h
Surface area = 2\u03c0rh
If radius is doubled and height is halved
![\"Surface](\"https:\/\/farm2.staticflickr.com\/1979\/31774683818_19bc973ae3_o.png\")
\u2234 Their surface area remain same (c)<\/p>\nQuestion 2.
Two cylindrical jars have their diameters in the ratio 3:1, but height 1:3. Then the ratio of their volumes is
(a) 1 : 4
(b) 1 : 3
(c) 3 : 1
(d) 2 : 5
Solution:
Sol. Ratio in the diameters of two cylinder = 3:1
and ratio in their heights = 1:3
Let radius of the first cylinder (r1<\/sub>) = 3x
and radius of second (r2<\/sub>) = x
and height of the first (h1<\/sub>) = y
and height of the second (h2<\/sub>) = 3y
Now volume of the first cylinder = \u03c0r2<\/sup>h
= \u03c0(3x)2<\/sup>\u00a0x y = 9\u03c0x2<\/sup>y
and of second cylinder = \u03c0(x2<\/sup>) (3y)
\u2234 Ratio between then = 9\u03c0x2<\/sup>y : 3\u03c0x2<\/sup>y
= 3 : 1 (c)<\/p>\nQuestion 3.
The number of surfaces in right cylinder is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
The number of surfaces of a right cylinder is three. (c)<\/p>\n
Question 4.
Vertical cross-section of a right circular cylinder is always a
(a) square
(b) rectangle
(c) rhombus
(d) trapezium
Solution:
The vertical cross-section of a right circular cylinder is always a rectangle. (b)<\/p>\n
Question 5.
If r is the radius and h is height of the cylinder the volume will be
![\"RD](\"https:\/\/farm2.staticflickr.com\/1907\/43828846390_62eab0519c_o.png\")
Solution:
Volume of a cylinder = \u03c0r2<\/sup>h (b)<\/p>\nQuestion 6.
The number of surfaces of a hollow cylindrical object is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
The number of surfaces of a hollow cylindrical object is 4. (d)<\/p>\n
Question 7.
If the radius of a cylinder is doubled and the height remains same, the volume will be
(a) doubled
(b) halved
(c) same
(d) four times
Solution:
If r be the radius and h be the height, then volume = \u03c0r2h
If radius is doubled and height remain same,
the volume will be
= \u03c0(2r)2<\/sup>h = \u03c0 x 4r2<\/sup>h
= 4\u03c0r2<\/sup>h = 4 x Volume
The volume is four times (d)<\/p>\nQuestion 8.
If the height of a cylinder is doubled and radius remains the same, then volume will be
(a) doubled
(b) halved
(c) same
(d) four times
Solution:
If r be the radius and h be the height, then volume of a cylinder = \u03c0r2<\/sup>h
If height is doubled and radius remain same, then volume = \u03c0r2<\/sup>(2h) = 2\u03c0r2<\/sup>h
\u2234 Its doubled (a)<\/p>\nQuestion 9.
In a cylinder, if radius is halved and height is doubled, the volume will be
(a) same
(b) doubled
(c) halved
(d) four times
Solution:
Let r be radius and h be height, then Volume = \u03c0r2<\/sup>h
If radius is halved and height is doubled
![\"RD](\"https:\/\/farm2.staticflickr.com\/1935\/44922117164_f5c4fd02d9_o.png\")
<\/p>\nQuestion 10.
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is
![\"RD](\"https:\/\/farm2.staticflickr.com\/1931\/43828846020_03e9cee139_o.png\")
Solution:
Let diameter of the base of a cylinder (r) = h
Then its height (h) = h
![\"RD](\"https:\/\/farm2.staticflickr.com\/1938\/44922116834_c33f2f8b95_o.png\")
<\/p>\n
Question 11.
A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m2<\/sup>, is
(a) 40\u03c0
(b) 80\u03c0
(c) 160\u03c0
(d) 200\u03c0
Solution:
Diameter of a cylindrical tunnel = 2 m
\u2234 Radius (r) =\u00a02<\/span>2<\/span><\/span><\/span><\/span><\/span>\u00a0= 1m
and length (h) = 40 m
Curved surfae area = 2\u03c0rh = 2 x \u03c0 x 1 x 40 = 80\u03c0 (b)<\/p>\nQuestion 12.
Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is
![\"Maths](\"https:\/\/farm2.staticflickr.com\/1934\/43828845860_defa65a8b4_o.png\")
Solution:
Let r1<\/sub>\u00a0and h1<\/sub>\u00a0be the radius and height of the
first cylinder, then
Volume = \u03c0r1<\/sub>2<\/sup>h1<\/sub>
Similarly r1<\/sub>\u00a0and h2<\/sub>\u00a0are the radius and height of the second cylinder
\u2234 Volume = \u03c0r2<\/sup>h2<\/sub>
But their volumes are equal,
![\"RD](\"https:\/\/farm2.staticflickr.com\/1913\/43828845840_4a74c885dd_o.png\")
<\/p>\nQuestion 13.
The radius of a wire is decreased to one- third. If volume remains the same, the length will become
(a) 3 times
(b) 6 times
(c) 9 times
(d) 27 times
Solution:
In the first case, r and h1, be the radius and height of the cylindrical wire
\u2234 Volume = \u03c0r2<\/sup>h1<\/sub>\u00a0\u2026(i)
In second case, radius is decreased to one third
![\"RD](\"https:\/\/farm2.staticflickr.com\/1968\/31774682238_9e6b052c5c_o.png\")
\u2234 In second case height is 9 times (c)<\/p>\nQuestion 14.
If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?
![\"RD](\"https:\/\/farm2.staticflickr.com\/1946\/43828845360_7976572e36_o.png\")
Solution:
Let r be the radius and h be the height then volume = \u03c0r2<\/sup>h
If height is doubled and volume is same and let x be radius then \u03c0r2<\/sup>h = \u03c0(x)2<\/sup>\u00a0x 2h
![\"RD](\"https:\/\/farm2.staticflickr.com\/1911\/31774681888_c2e8b7097f_o.png\")
<\/p>\nQuestion 15.
The volume of a cylinder of radius r is 1\/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?
![\"Surface](\"https:\/\/farm2.staticflickr.com\/1936\/31774681428_a8d86736e4_o.png\")
Solution:
Let r be the radius and h be the height, then volume = \u03c0r2<\/sup>h
This volume is\u00a01<\/span>4<\/span><\/span><\/span><\/span><\/span>\u00a0of the volume of a rectangular box
\u2234 Volume of box = 4\u03c0r2<\/sup>h
Let side of base of box = x and height h,
then volume = x2<\/sup>h
\u2234 4\u03c0r2<\/sup>h = x2<\/sup>h
![\"RD](\"https:\/\/farm2.staticflickr.com\/1933\/31774681218_9b9d537847_o.png\")
![\"Class](\"https:\/\/farm2.staticflickr.com\/1912\/31774681228_e38c0a0268_o.png\")
<\/p>\nQuestion 16.
The height ft of a cylinder equals the circumference of the cylinder. In terms of ft, what is the volume of the cylinder?
![\"Class](\"https:\/\/farm2.staticflickr.com\/1905\/43828844850_a73f0052c1_o.png\")
Solution:
In a cylinder,
h = circumference of the cylinder
![\"RD](\"https:\/\/farm2.staticflickr.com\/1938\/31774680878_7028f9e747_o.png\")
<\/p>\n
Question 17.
A cylinder with radius r and height ft is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?
(a) 2\u03c0r(r + h)
(b) \u03c0r(r + 2h)
(c) \u03c0r(2r + h)
(d) 2\u03c0r2<\/sup>\u00a0+ h
Solution:
r is the radius of the base and ft is the height of a closed cylinder
Then total surface area = 2\u03c0r(r + h ) (a)<\/p>\nQuestion 18.
The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?
![\"RD](\"https:\/\/farm2.staticflickr.com\/1922\/43828844590_e79962fb51_o.png\")
Solution:
Let h be the height and d be the diameter of a cylinder, then
![\"Surface](\"https:\/\/farm2.staticflickr.com\/1952\/45596601962_9ff1a4ff9a_o.png\")
<\/p>\n
Question 19.
Two steel sheets each of length a1<\/sub>\u00a0and breadth a2<\/sub>\u00a0are used to prepare the surfaces of two right circular cylinders \u2013 one having volume v1\u00a0<\/sub>and height a2<\/sub>\u00a0and other having volume v2<\/sub>\u00a0and height a1<\/sub>. Then,
![\"RD](\"https:\/\/farm2.staticflickr.com\/1946\/43828844300_ef29a44abf_o.png\")
Solution:
Length of each sheet = a1<\/sub>
and breadth = a2<\/sub>
Volume of cylinder = \u03c0r2<\/sup>h
In first case,
v1<\/sub>\u00a0is volume and a2<\/sub>\u00a0is the height
![\"RD](\"https:\/\/farm2.staticflickr.com\/1964\/43828844190_0a274d4e3c_o.png\")
![\"RD](\"https:\/\/farm2.staticflickr.com\/1979\/43828844050_4593e672e3_o.png\")
<\/p>\nQuestion 20.
The altitude of a circualr cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is
![\"RD](\"https:\/\/farm2.staticflickr.com\/1926\/43828843970_34e26d1749_o.png\")
Solution:
In first case,
Let r be the radius and h be the height of the cylinder. Then,
\u2234 Lateral surface area = 2\u03c0rh
In second case,
![\"Maths](\"https:\/\/farm2.staticflickr.com\/1905\/43828843910_8300ed8f29_o.png\")
<\/p>\n
We have included all the information regarding CBSE<\/a> RD Sharma Class 9 Solutions Chapter 19 MCQS<\/span>. If you have any query feel free to ask in the comment section.\u00a0<\/span><\/p>\n
![\"RD](\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-9-Solutions-Chapter-19-MCQS.jpg\")
<\/p>\n