Question

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

Answer 1

Diameter of the ductile metal = 1 cm
Radius of the ductile metal = 0.5 cm
Volume of the ductile metal = πr²(length) = π(0.5 cm)²(5 cm) = 1.25π cm³
Ductile metal is drawn into a wire of diameter 1 mm.
Radius of the wire = 0.5 mm = 0.05 cm

\[\text{ Length of wire }= \frac{1 . 25\pi {cm}^3}{\pi \left( 0 . 05 cm \right)^2} = 500 cm = 5 m\]

Thus, the length of wire is 5 m.