A hollow spherical shell is 2 cm thick. If its outer radius is 8 cm, then find the volume of the metal to make such a shell.

Outer radius = r₁ = 8 cm

The shell is 2 cm thick therefore we must subtract 2 cm from outer radius to get the inner radius

Inner radius = r₂ = 8 – 2 = 6 cm

Volume of metal required to make shell = volume of shell

Volume of shell we can get by subtracting the volume of hollow part of sphere from the complete volume of sphere with 8 cm radius

⇒ Volume of shell = πr₁³ – πr₂³

= π × (r₁³ – r₂³)

Substituting values

⇒ Volume of shell = × × (8³ – 6³)

= × × (512 – 216)

= × × 296

=

= 1240.38 cm³

Therefore, volume of the metal to make the shell is 1240.38 cm³