A right triangle has base $9\text{cm}$ and height $12\text{cm}$. When it is rotated about its height, it forms a solid. What is the volume of the solid? Take $\pi =\frac{22}{7}$. Choose the correct option.

Step-by-step solution

1. Rotating the triangle about its height generates a cone with radius equal to the base ($r=9\text{cm}$) and height equal to the given height ($h=12\text{cm}$).
2. Use the volume formula for a cone: $V=\frac{1}{3}\pi r^{2}h$.
3. Compute $r^2=9^2=81$.
4. Calculate $\frac{1}{3}\times \pi \times 81\times 12$.
5. First multiply $81\times 12=972$.
6. Divide by 3: $972/3=324$.
7. Thus $V=324\pi {\text{cm}}^3$.
8. The correct option is (b).

Concept tested: Volume of cone by rotation

Published 28 September 2026 · How this solution was prepared and checked

Related questions

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• 3 Find the total surface area of a solid sphere of radius 5 cm. Take π=22/7 and give the answer to the nearest square centimetre.
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