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.

• A. 0.67mm(approx..)
• B. 0.67cm(approx..)
• C. 0.67m(approx..)
• D. 67cm

Answer 1

The correct option is A

0.67mm(approx..)

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

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.).