# Volume of a Sphere

## Trending Questions

**Q.**

How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions?

**Q.**

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone.

**Q.**Question 1

If the radius of a sphere is 2r, then its volume will be:

A) 43πr3

B) 4πr3

C) 83πr3

D) 323πr3

**Q.**A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. The number of lead shots dropped in the vessel is :

- 50
- 25
- 100
- 150

**Q.**

The surface area of a cube is equal to the surface area of a sphere. The ratio of their volumes will be

π:3

6:5π

√3:√4π

√π:√6

**Q.**A sphere and cube have equal surface areas. Find the ratio of the volume of the sphere to that of cube.

**Q.**A solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water, of height 180 cm and radius 60 cm. Find the volume of water left in the cylinder, in cubic metres. [CBSE 2015]

**Q.**Choose the correct answer of the following question:

A metallic solid sphere of radius 9 cm is melted to form a solid cylinder of radius 9 cm. The height of the cylinder is

(a) 12 cm (b) 18 cm (c) 36 cm (d) 96 cm [CBSE 2014]

**Q.**

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres ?

**Q.**

The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

**Q.**If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, the diameter of the sphere is

(a) 12 cm

(b) 24 cm

(c) 30 cm

(d) 36 cm

**Q.**

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

**Q.**

**Three tennis balls are stored in a cylindrical container with a height of **$8$** inches and a radius of **$1.43$** inches. **

**The circumference of a tennis ball is **$8$** inches.**

**Find the amount of space within the cylinder not taken up by the tennis balls?**

**Q.**

How many shots each having diameter of 3 cm can be made from a cuboidal lead solid of dimensions 9 cm×11 cm×12 cm ?

**Q.**

Find the volume of a sphere of diameter 6 cm.

**Q.**

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the ratio of S and S'.

1:7

2:9

1:9

1:5

**Q.**

**Q.**

A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 cm2 and its height 12 cm, determine the radius of any of the spheres.

**Q.**

The diameter of a copper sphere is 6 cm. The sphere is melted and recast into a wire. If the length of the wire is 36 cm, its radius is

3 mm

5 mm

1 cm

5 cm

**Q.**

The volume of a sphere is 4851 cm3. Find its curved surface area.

**Q.**

A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are formed?

**Q.**A hemispherical bowl of diameter 7.2 cm is filled completely with chocolate sauce. This sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone. [3 MARKS]

**Q.**

Twenty-seven solid iron spheres, each of radius $r$ and surface area $S$ are melted to form a sphere with surface area $S$. Find the radius $r$ of the new sphere,

**Q.**

The radius of the cylinder of maximum volume, which can be inscribed in a sphere of the radius $R$is

$\frac{2}{3}R$

$\sqrt{\frac{2}{3}}R$

$\frac{3}{4}R$

$\frac{\sqrt{3}}{4}R$

**Q.**

**Q.**

The surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of their volumes.

**Q.**

The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

225200π cm3

105000π cm3

15200π cm3

115200π cm3

**Q.**

The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is

8.4

1.05

4.2

2.1

**Q.**

If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

2:1

1:4

1:2

4:1

**Q.**Find the number of balls each of radius 1cm . Can be made from a solid sphere of lead of radius 6cm