A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire, is :

Solution (By Examveda Team)

Volume of copper rod :
$$\eqalign{ & = \left( {\pi \times \frac{1}{2} \times \frac{1}{2} \times 8} \right){\text{ c}}{{\text{m}}^3} \cr & = 2\pi \,{\text{ c}}{{\text{m}}^3} \cr} $$
Let the radius of the wire be r cm
Then, volume of wire :
$$\eqalign{ & = \left( \pi {r^2} \times 1800 \right) {\text{cm}}^3 \cr & = 1800\, \pi {r^2} {\text{ cm}}^3 \cr & \therefore 1800\pi {r^2} = 2\pi \cr & \Rightarrow {r^2} = \frac{2}{{1800}} \cr & \Rightarrow {r^2} = \frac{1}{{900}} \cr & \Rightarrow r = \sqrt {\frac{1}{{900}}} = \frac{1}{{30}} \cr} $$