Question

The internal and external radii of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recasts into a solid right circular cylinder of base radius 7 cm. Find the height of the cylinder.

Answer 1

Volume of spherical shell = Volume of outer sphere − Volume of inner sphere

= `(4/3)π(5^3) − (4/3)π(3^3)`

= `(4/3)π(125 − 27)`

= `(4/3)π × 98`

= `(392/3)π cm^3`

Let h be the height of the cylinder. Volume of the solid right circular cylinder

= π × (base radius)² × h

= π × 7² × h 

= 49π × h cm³

Metal is conserved, so equate volumes:

`49π × h = (392/3)π`

`49h = 392/3`

⇒ h = `(392/3) ÷ 49 = 8/3 cm`   ...[Cancel π and solve for h]

`h = 8/3 cm ≈ 2.67 cm or 2 2/3 cm`