The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of wire.

Given,

Diameter of the sphere = 6 cm

So, its radius (R) = $\dfrac{6}{2}$ = 3 cm

Diameter of cylindrical wire = 0.2 cm

So, the radius of the wire (r) = $\dfrac{0.2}{2}$ = 0.1 cm

Let length of wire = h

Since, sphere is melted and recasted into a wire.

∴ Volume of sphere = Volume of wire

$\Rightarrow \dfrac{4}{3}πR^3 = πr^2h \\[1em] \Rightarrow h = \dfrac{\dfrac{4}{3}πR^3}{πr^2} \\[1em] \Rightarrow h = \dfrac{4R^3}{3r^2} \\[1em] \Rightarrow h = \dfrac{4 \times 3^3}{3 \times (0.1)^2} \\[1em] \Rightarrow h = \dfrac{4 \times 3^2}{0.01} \\[1em] \Rightarrow h = 4 \times 3^2 \times 100 \\[1em] \Rightarrow h = 3600 \text{ cm} \\[1em] \Rightarrow h = 3600 \times \dfrac{1}{100} \text{ m} \\[1em] \Rightarrow h = 36 \text{ m}.$

Hence, length of the wire = 36 m.