Question

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm. It is drawn-out into a wire of diameter 1 mm. What will be the length of the wire so formed?

Answer 1

We have,

Diameter of metallic cylinder = 1 cm

Radius of metallic cylinder = d/2 = 1/2 = 0.5 cm

Length of cylinder = 5 cm

Diameter of wire drawn from it = 1 mm = 0.1 cm

Radius of wire = 0.5mm = 0.05cm

Let length of wire be ‘h’ cm

Length of wire drawn from metal = volume of metal/ volume of wire

= πr²h / πr²

= (½)² × 5 / (0.05)²

= (5/4) / 0.0025

= 1.25/0.0025

= 500 cm

= 5m

∴ Length of the wire is 5m.