Question

A solid metal cylinder with a length of 24 cm and radius 2cm is melted down to a form of sphere . what is the radius of the sphere.

Answer 1

Given:

Height of the cylinder (h) = 24 cm

Radius of the cylinder (r) = 2 cm.

If the shape of an object is changed it's Volume doesn't change.

So,

Volume of cylinder = Volume of sphere

Volume of cylinder = πr²h

Volume of sphere = 4/3 πr³

Let the radius of the sphere be r'

⟶ π * (2)² * 24 = 4/3 * π * (r')³

⟶ 4 * 24 * 3/4 = (r')³

⟶ 72 = (r')³

⟶ (4.16)³ = (r')³

⟶ 4.16 = r'

∴ The radius of the sphere is 4.16 cm.