Question

The outer diameter of a spherical shell is 12cm and its inner diameter is 8cm. Find the volume of metal contained in the shell. Also, find its outer surface area.

Answer 1

It is given that

Outer diameter of spherical shell = 12cm

Radius of spherical shell = 12/2 = 6cm

Inner diameter of spherical shell = 8cm

Radius of spherical shell = 8/4 = 2cm

We know that

Volume of outer shell = 4/3 πr³

By substituting the values

Volume of outer shell = 4/3 × (22/7) × 6³

So we get

Volume of outer shell = 905.15 cm³

Volume of inner shell = 4/3 πr³

By substituting the values

Volume of outer shell = 4/3 × (22/7) × 4³

So we get

Volume of outer shell = 268.20 cm³

So the volume of metal contained in the shell = Volume of outer shell – Volume of inner shell

By substituting the values

Volume of metal contained in the shell = 905.15 – 268.20 = 636.95 cm³

We know that

Outer surface area = 4πr²

By substituting the values

Outer surface area = 4 × (22/7) × 6²

On further calculation

Outer surface area = 452.57 cm²

Therefore, the volume of metal contained in the shell is 636.95 cm³ and the outer surface area is 452.57 cm².