Question

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire. [1 MARK]

Answer 1

Concept: 1 Mark

The volume of the rod $=\pi \times {\left(\frac{1}{2}\right)}^2\times 8c{m}^3=2\pi c{m}^3$

The length of the new wire of the same volume = 18 m = 1800 cm

If r is the radius (in cm) of cross-section of the wire, its volume $=\pi \times r^2\times 1800c{m}^3$

Therefore, $\pi \times r^2\times 1800=2\pi$

i.e., $r^2=\frac{1}{900}$

i.e., $r=\frac{1}{30}$

So, the diameter of the cross section, i.e., the thickness of the wire is $\frac{1}{15}cm$,

i.e., 0.67mm (approx.).