Question

A copper sphere of diameter 6 cm is melted and drawn into 36 cm long wire of uniform circular cross-section. Then, its radius is
(a) 2 cm
(b) 1.5 cm
(c) 1.2 cm
(d) 1 cm

Answer 1

(d) 1 cm

Ler r cm be the radius of the wire.
Diameter of the copper sphere = 6 cm
i.e., radius of the copper sphere = 3 cm
Length of the wire= 36 cm
The sphere is melted and drawn into a wire.
Then volume of wire = volume of copper sphere
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^2\times 36=\frac{4}{3}\mathrm{\pi }\times 3^3 \\ \Rightarrow r^2=\frac{4\times 9}{36}=1 \\ \Rightarrow r=1\mathrm{cm} \end{gathered}$$

Hence, the radius of the wire is 1 cm.