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If h is height and \( \Large \alpha \) is semivertical angle of a right circular cone, then its volume is given by

A) \( \Large \frac{1}{3} \pi h^{3} \tan^{2} \alpha \)
B) \( \Large \frac{1}{3} \pi h^{2} \tan^{2} \alpha \)
C) \( \Large \frac{1}{3} \pi h^{3} \tan^{3} \alpha \)
D) \( \Large \frac{1}{3} \pi h^{2} \tan^{3} \alpha \)

Correct Answer:

A) \( \Large \frac{1}{3} \pi h^{3} \tan^{2} \alpha \)

Description for Correct answer:

\( \Large \tan \alpha = \frac{r}{h} \)

=> \( \Large r = h \tan \alpha \)

\( \Large V = \frac{1}{3} \pi r^{2}h \)

=> \( \Large V = \frac{1}{3} \pi \left(h \tan \alpha \right)^{2}h \)

= \( \Large \frac{1}{3} \pi h^{3} \tan^{2} \alpha \)

Part of solved Mensuration questions and answers : >> Aptitude >> Mensuration

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