#### Chapter 21 Surface Area and Volume of a Sphere R.D. Sharma Solutions for Class 9th MCQ's

Multiple Choice Questions

1. In a sphere the number of faces is
(a) 1
(b) 2
(c) 3
(d) 4

Solution

The number of faces is 1.

2. The total surface area of hemisphere of radius r.
(a) Ï€r2
(b) 2Ï€r2
(c) 3Ï€r2
(d) 4Ï€r2

Solution
So, here we have to find total surface area, which is sum of curved surface area and top area. So total surface area is 2Ï€r2 + Ï€r2 = 3Ï€r2

3. The ratio of the total surface area of a sphere and a hemisphere of same radius is
(a) 2:1
(b) 3:2
(c) 4:1
(d) 4:3

Solution

Total Surface Area of sphere = 4Ï€r2
Total Surface Area of hemisphere = 3Ï€r2
The Ratio is (4Ï€r2)/(3Ï€r2) = 4/3
So, option (d) is correct

4. A Sphere and a cube are of the same height. The ratio of their volumes is
(a) 3:4
(b) 21:11
(c) 4:3
(d) 11:21

Solution

5. The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
(a) 27Ï€ cm3
(b) 36Ï€ cm3
(c) 108 cm3
(d) 12Ï€ cm3

Solution

6. A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
(a) 4
(b) 3
(c) 6
(d) 8

Solution

7. If the ratio of volumes of two sphere is 1:8, then ratio of their surface area is
(a) 1:2
(b) 1:4
(c) 1:8
(d) 1:16

Solution

8. If the surface area of a sphere is 144Ï€ m2, then its volume in (m3) is
(a) 288Ï€
(b) 316 Ï€
(c) 300Ï€
(d) 188Ï€

Solution

9. If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
(a) 100
(b) 75Ï€
(c) 60Ï€
(d) 50Ï€

Solution

10. The ratio between volume of a sphere and volume of circumscribing right circular cylinder is
(a) 2:1
(b) 1:1
(c) 2:3
(d) 1:2

Solution

11. If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of cube is
(a) Ï€ :2
(b) Ï€:3
(c) Ï€:4
(d) Ï€:6

Solution

12. If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone
(a) 2r
(b) 3r
(c) r
(d) 4r

Solution

13. A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of sphere is r, the volume of cylinder is
(a) 4Ï€r3
(b) 8/3 Ï€r3
(c) 2Ï€r3
(d) 8Ï€r3

Solution

14. A cone and a hemisphere have equal bases and equal volumes, the ratio of their heights is
(a) 1:2
(b) 2:1
(c) 4:1
(d) √2: 1

Solution

15. A cone and a hemisphere and a cylinder stand on the equal bases and have the same height . The ratio of their volumes is
(a)1:2:3
(b) 2:1:3
(c) 2:3:1
(d) 3:2:1

Solution

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