Volume of Sphere and Hemisphere – Formula and Examples

Here you will learn what is the formula for volume of sphere and hemisphere with examples based on it.

Let’s begin – 

Formula for Volume of Sphere and Hemisphere

(i) Volume of Sphere Formula

Volume of sphere = ${4\over 3}\pi r^3$

where r is the radius of sphere.

(ii) Volume of Hemisphere Formula

Volume of Hemisphere = ${2\over 3}\pi r^3$

where r is the radius of hemisphere.

Example : Find the volume of a sphere of radius 11.2 cm. 

Solution : Here, radius = 11.2 cm

Volume of Sphere = ${4\over 3}\pi r^3$

= ${4\over 3} \times {22\over 7} \times (11.3)^3$ = 5888.72 $cm^3$

Example :  A hemispherical bowl has a radius of 3.5 cm. What would be the volume of water it would contain?

Solution : Here, radius = 3.5 cm

 The volume of water the bowl can contain = ${2\over 3}\pi r^3$

= ${2\over 3} \times {22\over 7} \times (3.5)^3$ = 89.8 $cm^3$

Example :  A shot-putt is a metallic sphere of radius 4.9 cm. If the density of the metal is 7.8 g per $cm^3$, find the mass of the shot-putt.

Solution : Since the shot-putt is a solid sphere made of metal and its mass is equal to the product of its volume and density, we need to find the volume of the sphere.

Now, Volume of the Sphere = ${4\over 3}\pi r^3$

= ${4\over 3} \times {22\over 7} \times (4.9)^3$ = 493 $cm^3$

Further mass of 1 $cm^3$ of metal is 7.8 g.

Therefore, mass of the shot-putt = 7.8 $\times$ 493 = 3845.44 gm = 3.85 kg