Discussion
Sam has a solid metal ball with diameter 6cm. He melts it and uses the material for making a solid cylinder. If the diameter of the cylinder is same as the ball, what would its height be?
Answer: A
Melting conserves volume, and the two shapes share the same radius \( r = 3 \) cm.
\[ V_{\text{sphere}} = \frac{4}{3}\pi r^{3} = \frac{4}{3}\pi (27) = 36\pi \text{ cm}^{3} \]
\[ V_{\text{cylinder}} = \pi r^{2} h = 9\pi h \]
\[ 9\pi h = 36\pi \quad\Longrightarrow\quad h = 4 \text{ cm} \]
Whenever a sphere is recast as a cylinder of the same radius, the height is always \( \tfrac{4}{3}r \) - here \( \tfrac{4}{3} \times 3 = 4 \).
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