Volume of a Sphere

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) $\frac{4}{3}\pi r^3$
B) $4\pi r^3$​​​​​​​
C) $\frac{8}{3}\pi r^3$​​​​​​​
D) $\frac{32}{3}\pi r^3$​​​​​​​

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 :

1. 50
2. 25
3. 100
4. 150

Q.

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

1. $\pi :3$

2. $6:5\pi$

3. $\sqrt{3}:\sqrt{4}\pi$

4. $\sqrt{\pi }:\sqrt{6}$

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 $3cm$ can be made from a cuboidal lead solid of dimensions $9cm\times 11cm\times 12cm$ ?

Q.

Find the volume of a sphere of diameter $6cm$.

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. 1:7

2. 2:9

3. 1:9

4. 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 $c{m}^2$ 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

1. 3 mm

2. 5 mm

3. 1 cm

4. 5 cm

Q.

The volume of a sphere is 4851 $c{m}^3$. 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

1. $\frac{2}{3}R$

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

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

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

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?

1. $225200\pi c{m}^3$

2. $105000\pi c{m}^3$

3. $15200\pi c{m}^3$

4. $115200\pi c{m}^3$

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

1. 8.4

2. 1.05

3. 4.2

4. 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

1. 2:1

2. 1:4

3. 1:2

4. 4:1

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