#### 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) πr

^{2}
(b) 2πr

^{2}
(c) 3πr

^{2}
(d) 4πr

^{2}**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 2πr

^{2}+ πr^{2}= 3πr^{2}
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 = 4πr

^{2}
Total Surface Area of hemisphere = 3πr

^{2}
The Ratio is (4πr

^{2})/(3πr^{2}) = 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) 27π cm

^{3}
(b) 36π cm

^{3}
(c) 108 cm

^{3}
(d) 12π cm

^{3}**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 144π m

^{2}, then its volume in (m^{3}) is
(a) 288π

(b) 316 π

(c) 300π

(d) 188π

**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) 75π

(c) 60π

(d) 50π

**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) π :2

(b) π:3

(c) π:4

(d) π: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) 4πr

^{3}
(b) 8/3 πr

^{3}
(c) 2πr

^{3}
(d) 8πr

^{3}**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**