Question

A hollow cylinder of external diameter 18 cm, 1 cm thick and 10 cm long is melted and recast into a solid cylinder diameter 2 cm. Find the length of the cylinder.

Answer 1

Given:

External diameter of hollow cylinder (D) = 18 cm

External radius R = `18/2` = 9 cm 

Thickness = 1cm

Internal radius r = R − thickness = 9 − 1 = 8cm

Length of hollow cylinder (h) = 10 cm

Diameter of the solid cylinder = 2 cm

Radius of solid cylinder (rs) = `2/2` = 1 cm

Volume of the hollow cylinder 

V = `π (R^2 − r^2) h`

= `π (9^2 − 8^2) × 10`

= `π (81 − 64) × 10`

= π × 17 × 10

= 170π cm³

Let L be the length of the new solid cylinder. Its radius

= `2/2` = 1 cm, so its volume

= π (1)² L = π L

Equate volumes (metal conserved):

π L = 170π

⇒ L = 170

Therefore, the length of the solid cylinder = 170 cm.