# PRACTICE QUESTIONS ON SPHERES

### Examination Questions on Spheres

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1. If 64 identical small spheres are made out of a big sphere of diameter 8 cm, what is the surface area of each small sphere?

1. π cm2
2. 2π cm2
3. 4π cm2
4. 8π cm2

2. What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 square cm?

1. 14 cm
2. 10.5 cm
3. 7 cm
4. 3.5 cm

3. What is the volume of the largest sphere that can be carved out of a cube of edge 3 cm?

1. 9π cubic cm
2. 6π cubic cm
3. 4.5π cubic cm
4. 3π cubic cm

4. If the ratio of the diameters of two spheres is 3 : 5, then what is the ratio of their surface areas?

1. 9 : 25
2. 9 : 10
3. 3 : 5
4. 27 : 125

5. A right circular metal cone (solid) is 8 cm high and the radius is 2 cm. It is melted and recast into a sphere. What is the radius of the sphere?

1. 2 cm
2. 3 cm
3. 4 cm
4. 5 cm

6. Let the largest possible right circular cone and largest possible sphere be fitted into two cubes of same length. Let C and S denote the volume of cone and volume of sphere respectively, then which one of the following is correct?

1. C = 2S
2. S = 2C
3. C = S
4. C = 3S

7. If the surface area of a sphere is 616 square cm, what is its volume?

1. 4312/3 cubic cm
2. 4102/3 cubic cm
3. 1257 cubic cm
4. 1023 cubic cm

8. The surface area of a sphere is 616 square cm. If its radius is changed so that the area gets reduced by 75%, then the radius becomes

1. 1.6 cm
2. 2.3 cm
3. 2.5 cm
4. 3.5 cm

9. If the diameter of a sphere is doubled, how does its surface area change?

1. It increases two times
2. It increases three times
3. It increases four times
4. It increases eight times.

10. A sphere is inscribed in a cubical box such that the sphere is tangent to all six faces of the box. What is the ratio of the volume of the cubical box to the volume of sphere?

1. 36π
2. 4π/3
3. 6/π

11. What is the number of wax balls, each of radius 1 cm, that can be molded out of a sphere of radius 8 cm?

1. 256
2. 512
3. 768
4. 1024

12. Assume the Earth to be a sphere of radius R. What is the radius of the circle of latitude 40° S?

1. R cos 40°
2. R sin 80°
3. R sin 40°
4. R tan 40°

13. What is the volume (in cm3) of a spherical shell with 8 cm and 10 cm as its internal and external diameters respectively?

1. 61π/3
2. 122π/3
3. 244π/3
4. 250π/3

14. The volume of a sphere is 8 times that of another sphere. What is the ratio of their surface areas?

1. 8 : 1
2. 4 : 1
3. 2 : 1
4. 4 : 3

15. A sphere and a cube have same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube?

1. π : 6
2. 1 : 1
3. 6 : π
4. 3 : π

16. If a sphere of radius 10 cm is intersected by a plane at a distance 8 cm from its centre, what is the radius of the curve of intersection of the plane and the sphere?

1. 8 cm
2. 6 cm
3. 5 cm
4. 4 cm

17. If the number of square centimeters on the surface area of a sphere is three times the number of cubic centimeters in its volume, then what is its diameter?

1. 1 cm
2. 2 cm
3. 3 cm
4. 6 cm

18. A sphere is cut into two equal halves and both the halves are painted from all the sides. The radius of the sphere is r units and the rate of painting is Rs 8 per sq. unit. What is the total cost of painting the two halves of the sphere in rupees?

1. 6πr2
2. 32πr2
3. 48πr2