# Volume of sphere questions

In this chapter, we will discuss questions related to volume of sphere and its solution.

The formula for volume of sphere is given as;

Volume = \mathtt{\ \frac{4}{3} .\pi .r^{3}}

Where, r is the radius of sphere.

## Questions on volume of sphere

Question 01
The radius of sphere is given as 21 cm. Find the volume.

Solution

Volume = \mathtt{\ \frac{4}{3} .\pi .r^{3}}

Putting the values;

\mathtt{Volume\ =\ \frac{4}{3} \times \frac{22}{7} \times ( 21)^{3}}\\\ \\ \mathtt{Volume\ =\ 38808\ \ cm^{3}}

Hence, 38808 cu cm is the volume of sphere.

Question 02
Find the volume of sphere with diameter 14 cm.

Solution
Diameter (d) = 14 cm
Radius (r) = 14 / 2 = 7 cm

Volume of sphere is given by following formula;

Volume = \mathtt{\ \frac{4}{3} .\pi .r^{3}}

Putting the values in formula;

\mathtt{Volume\ =\ \frac{4}{3} \times \frac{22}{7} \times ( 7)^{3}}\\\ \\ \mathtt{Volume\ =\ 1437.33\ \ cm^{3}}

Hence, 1437.33 cu cm is the volume of cube.

Question 03
A hemisphere tank of 3 meter is given. Find the volume of water (in liters) that can be stored in the tank.

Solution

We know that when sphere is cut into half, we get two hemisphere. Hence, the volume of hemisphere is half of the sphere.

Volume of hemisphere = \mathtt{\frac{1}{2} .\ \frac{4}{3} .\pi .r^{3}

Putting the values, we get;

\mathtt{Volume\ =\frac{1}{2} \times \frac{4}{3} \times \frac{22}{7} \times ( 3)^{3}}\\\ \\ \mathtt{Volume\ =\ 56.57\ \ m^{3}}

Hence, 56.57 cu meter of water can be stored in the tank.

Now converting the volume into liters.

1 cu m = 1000 liters

56.57 cu. m = 56570 liters

So, total of 56570 liters of water is stored in the hemi sphere.

Question 04
A cube of lead of size 21 cm is given. How many spherical bullets of radius 3 cm can be made from the given lead cube.

Solution
First calculate the volume of lead into the given cube.

Volume of cube = side x side x side

Volume of cube = 21 x 21 x 21 = 9261 cu. cm

So from 9261 cu cm of the cube, the spherical bullets will be made.

Let ” n ” number of spherical bullets (radius 3 cm) are made from the above cube.

Volume of all bullets = volume of cube

\mathtt{n\times \frac{4}{3} .\pi .r^{3} \ =\ 9261}\\\ \\ \mathtt{n\times \frac{4}{3} \times \frac{22}{7} \times ( 3)^{3} =\ 9261}\\\ \\ \mathtt{n\ =\ \frac{9261\times 21}{4\times 22\times 27}}\\\ \\ \mathtt{n\ =\ \frac{194481}{2376} =81.8\ bullets}

Hence, total of 81 bullets are made from cube.

Question 05
A shopkeeper has spherical chocolate of radius 5 cm. He breaks the chocolate and with the same material he started making chocolate sphere of radius 2.5 cm. Find how many small spheres can be made ?

Solution
Let ” n ” number of small spheres can be manufactured.

Volume of big sphere = n x volume of small sphere

\mathtt{\frac{4}{3} .\pi .( 5)^{3} \ =\ n\times \frac{4}{3} .\pi .( 2.5)^{3}}\\\ \\ \mathtt{n\ =\ \frac{5^{3}}{2.5^{3}} \ }\\\ \\ \mathtt{n=\ 8}

Hence, total of 8 small spheres can be made from the large one.

Question 06
A cylindrical vessel half filled with water is given. A spherical ball of radius 5 cm is immersed in the vessel which results in rise of water level by 5/3 cm. Find the radius of cylindrical vessel.

Solution
Radius of sphere (r) = 5 cm

Here the volume of rise in water level is equal to the volume of sphere.

Volume of rise in water level = volume of sphere

\mathtt{\pi .R^{2} .\left(\frac{5}{3}\right) =\frac{4}{3} .\pi .( 5)^{3}}\\\ \\ \mathtt{R^{2} =4 \times 5^{2}}\\\ \\ \mathtt{R\ =\ 2\times 5=\ 10\ cm\ }

Hence, the radius of cylindrical vessel is 10 cm.

Question 07
A sphere of radius 3 cm is melted and drawn into cylindrical wire of radius 0.1 cm. Find the length of wire formed?

Solution
Sphere radius (r) = 3 cm
Wire radius (R) = 0.1 cm

Here the material used in the sphere is converted into cylindrical wire.

Volume of wire = volume of sphere

\mathtt{\pi .R^{2} .h=\frac{4}{3} .\pi .( r)^{3}}\\\ \\ \mathtt{\pi .( 0.1)^{2} .h=\frac{4}{3} .\pi .( 3)^{3}}\\\ \\ \mathtt{h\ =\ \frac{4}{3} \times \frac{3^{3}}{0.1^{2}}}\\\ \\ \mathtt{h\ =\ 3600\ cm\ }

Hence, the length of wire is 3600 cm.