Question

The diameter of a metallic sphere is 12 mm. It is melted and recast into a wire of diameter 0.4 mm. Find the length of the wire.

Answer 1

Given:

Diameter of sphere = 12 mm ⇒ radius R = 6 mm.

Diameter of wire = 0.4 mm ⇒ radius r = 0.2 mm.           ...[Use conservation of volume: volume of sphere = volume of wire.]

Volume of sphere = `(4/3)πR^3`

= `(4/3)π(6^3)`

= 288π mm³.

Volume of wire (cylindrical)

= `πr^2 xx L`

= π(0.2^2) xx L

= 0.04π × L mm³.

Equate volumes: 288π = 0.04π × L 

⇒ L = `288/0.04`

= 7200 mm.

Convert to metres: 7200 mm

= `7200/1000`

= 7.2 m.