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A right triangle has a base of $9, cm$ and a height of $12, cm$ . When the triangle is rotated about its base, it forms a right circular cone. What is the volume of the resulting solid? (Take $π = \frac{22}{7}$ ).

hard MCQ 3 marks Class 10 · Mathematics · Surface Areas and Volumes

(a) $432 π, cm^{3}$
(b) $648 π, cm^{3}$
(c) $288 π, cm^{3}$
(d) $216 π, cm^{3}$

Answer

(a)

432 π, cm^{3}

The correct answer is (a) $432 π, cm^{3}$ — Thus $V = 432 π, cm^{3}$ .

Step-by-step solution

Rotating about the base makes a right circular cone.
The radius of the cone equals the triangle’s height: $r = 12$ cm.
The height of the cone equals the triangle’s base: $h = 9$ cm.
Volume of a cone: $V = \frac{1}{3} π r^{2} h$ .
Substitute $r = 12$ , $h = 9$ : $V = \frac{1}{3} π (12)^{2} (9)$ .
Compute $1 2^{2} = 144$ and $144 \times 9 = 1296$ .
Divide by $3$ : $1296/3 = 432$ .
Thus $V = 432 π, cm^{3}$ .

Common mistake: Confusing base and height of the triangle

Concept tested: Cone volume by rotation

Published 1 October 2026 · How this solution was prepared and checked

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