A solid metal ball of radius 9 cm is melted and drawn into a wire of radius 1.5 mm…

Step 1. The units. $1.5\ \text{mm} = 0.15\ \text{cm}$.

Step 2. The ball. $\dfrac{4}{3}\pi \times 9^3\ \text{cm}^3 = 972\pi\ \text{cm}^3$.

Step 3. The wire. $\pi \times (0.15\ \text{cm})^2 \times L = 0.0225\pi L\ \text{cm}^2$.

Step 4. Equate. $0.0225\pi L = 972\pi$, so $L = 43\,200\ \text{cm}$.

Step 5. In metres. $43\,200\ \text{cm} = 432\ \text{m}$.