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Q.

A right triangle with sides 5 cm, 12 cm, and 13 cm is revolved about the side 12 cm. Then the volume of the cone thus formed is

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a

$392 \frac{1}{3} {cm}^{3}$

b

$300 \frac{5}{8} {cm}^{3}$

c

$258 {cm}^{3}$

d

$314 \frac{2}{7} {cm}^{3}$

answer is A.

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Detailed Solution

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$h = 12 cm$

$r = 5 cm$
Volume $= \frac{1}{3} π r^{2} h$

$= \frac{1}{3} \times \frac{22}{7} \times 25 \times 12$

$= \frac{2200}{7}$

$= 314 \frac{2}{7} {cm}^{3}$

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A right triangle with sides 5 cm, 12 cm, and 13 cm is revolved about the side 12 cm. Then the volume of the cone thus formed is