Question

Find the weight of a spherical shell of copper having external diameter 30 cm and thickness of 2 cm. Density of copper is 10 g/cm³.

Answer 1

Given:

External diameter = 30 cm ⇒ external radius R = 15 cm.

Thickness = 2 cm ⇒ internal radius r = R − 2 = 13 cm.

Density of copper = 10 g/cm³.

Volume of the spherical shell = `(4/3)π(R^3 − r^3)`

R³ = 15³ = 3375 cm³   ...[Compute the cubes]

r³ = 13³ = 2197 cm³

R³ − r³ = 3375 − 2197 = 1178 cm³

Volume = `(4/3)π × 1178`

= 4.19047619 × 1178   ...[Using π = `22/7`]

= 4936.381 cm³

Mass (weight) = density × volume

= 10 g/cm³ × 4936.381 cm³

= 49363.81 g

= 49363.81 g ≈ 49.364 kg   ...[Convert to kilograms]