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