Question

The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire of diameter 2 mm having uniform cross-section. Find the length of the wire.

Answer 1

Radius of sphere = 9 cm = 90 mm
volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.14\times {90}^3$

radius of wire = 1 mm
volume of wire(cylinder)$=\pi r^{2}h=3.14\times 1^2\times h$

if sphere is drawn to form wire
volume of sphere = volume of wire

=> $\frac{4}{3}\times 3.14\times {90}^3=3.14\times 1^2\times h$

=> $h=972000mm=\frac{972000}{1000}=972m$