A solid metallic cone is melted and recast into a solid cylinder with the same base as that of the cone. If the height of the cylinder is 7 cm, what is the height of the cone?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21 cm
When a solid is melted and recast, its volume does not change. A cone holds only one-third of a cylinder with the same base and height.
Volume of the cone \(\displaystyle =\frac{1}{3}\pi r^2H\); volume of the cylinder \(=\pi r^2\times7\)
\(\displaystyle \frac{1}{3}\pi r^2H=7\pi r^2\), so \(\displaystyle \frac{H}{3}=7\)
\(H=21\) cm
