The diameter of a copper sphere is 18 cm. It is melted and drown into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Given,

Diameter of sphere = 18 cm

Length of wire = 108 m = 10800 cm

Radius of copper sphere = m = 36 m

Volume of sphere = πr³ = × π × 9 × 9 × 9cm³ = 972π cm³

Let the radius of wire be r cm

= πr²l = πr² × 10800

But the volume of wire = volume of sphere

⇒ πr² × 10800 = 972π

r² = = 0.09 cm²

r = cm = 0.3

Hence, the diameter = 2r = 0.6 cm