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A solid sphere of radius 6 cm is melted and recast into three identical cones of equal height. If each cone's radius is 3 cm, what is the height of each cone?

1. 16 cm
2. 18 cm
3. 20 cm
4. 32 cm

Correct answer: 32 cm

Solution

Volume of sphere = \(\frac{4}{3}\pi(6^3)=288\pi\). Let the height of each cone be \(h\); total volume of 3 cones = \(3\times \frac{1}{3}\pi(3^2)h = 9\pi h\). Equating gives \(9\pi h = 288\pi\), so \(h=32\) cm.

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