A copper sphere of diameter 24 cm is melted and drawn into a wire of diameter 4 mm. What is the length (in metres) of the wire?

Step 1: Volume of sphere

Diameter of sphere = 24 cm
Radius = 12 cm

Volume of sphere:

$V=\frac{4}{3}\pi (12)^3$

$V=2304\pi$

Step 2: Volume of wire (cylinder)

Wire diameter = 4 mm = 0.4 cm
Radius = 0.2 cm

Volume of wire:

$V=\pi(0.2)^2 \times L$

$V=0.04\pi L$

Step 3: Equate volumes

$2304\pi=0.04\pi L$

$L=\frac{2304}{0.04}$

$L=57600\text{ cm}$

Convert into metres:

$L=\frac{57600}{100}=576\text{ m}$

Final Answer: 576 m