A solid metal cone has radius 12 cm and height 24 cm…

Step 1. The cone. $\dfrac{1}{3}\pi \times 144\ \text{cm}^2 \times 24\ \text{cm} = 1152\pi\ \text{cm}^3$.

Step 2. The cylinder. $\pi \times 64\ \text{cm}^2 \times h = 1152\pi\ \text{cm}^3$, so $h = 18\ \text{cm}$.

Step 3. One ball. $\dfrac{4}{3}\pi \times 27\ \text{cm}^3 = 36\pi\ \text{cm}^3$.

Step 4. The number. $1152\pi \div 36\pi = 32$.