A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 5 cm.

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.

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