A solid hemisphere of radius 6 cm is melted and recast into a solid cone with a base radius of 12 cm. What is the height of the cone?

Explanation

1. 01

   Hemisphere volume = $\frac{2}{3}\pi \times 6^3 = 144\pi$.

2. 02

   Cone volume = $\frac{1}{3}\pi \times 12^2 \times h = 48\pi h$.

3. 03

   $48\pi h = 144\pi$, so $h = 3$ cm.