A solid cone is formed by rotating a right triangle having base $12\text{cm}$ and height $9\text{cm}$ about its height. Find the volume of the cone. Give your answer in cubic centimeters, correct to the nearest ${\text{cm}}^3$.

Step-by-step solution

1. When the triangle rotates about its height, the base becomes the radius of the cone: $r=12\text{cm}$.
2. The given height of the triangle becomes the height of the cone: $h=9\text{cm}$.
3. Volume of a cone = $\frac{1}{3}\pi r^{2}h$.
4. Substitute $r$ and $h$: $V=\frac{1}{3}\pi \times 12^2\times 9=\frac{1}{3}\pi \times 144\times 9$.
5. Calculate: $\frac{1}{3}\times 144\times 9=432$, so $V=432\pi {\text{cm}}^3$.
6. Numerically, $432\pi \approx 1357{\text{cm}}^3$, which rounds to $1357{\text{cm}}^3$.

Concept tested: Volume of a cone

Published 20 August 2026 · How this solution was prepared and checked