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?

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Accepted Answer

1. Volume of sphere: $V_s=\frac{4}{3}\pi r^3=\frac{4}{3}\pi\cdot6^3=288\pi$.  
2. Volume of one cone: $V_c=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\cdot3^2\cdot h=3\pi h$.  
3. Three cones together: $3V_c=9\pi h$, set equal to sphere: $9\pi h=288\pi$.  
4. Solve for $h$: $h=288/9=32$ cm. So the height is 32 cm (option d).  
FINAL_ANSWER: d

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