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
$\mathrm{Length}\mathrm{of}\mathrm{wire}=\frac{1.25\mathrm{\pi }{\mathrm{cm}}^3}{\mathrm{\pi }{\left(0.05\mathrm{cm}\right)}^2}=500\mathrm{cm}=5\mathrm{m}$
Thus, the length of wire is 5 m.