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The volume of the greatest cone obtained by rotating a right-angled triangle of hypotenuse 2 units about a side is k π 9 3 cubic units, then the value of k is equal to

Correct answer

16

Step-by-step solution

The volume generated = V = 1 3 π r 2 h = 1 3 π 4 - x 2 x For maximum volume, d V d x = 0 ⇒ 4 - 3 x 2 = 0 ⇒ x = 2 3 V m a x = π 3 4 - 4 3 2 3 = 16 π 9 3 Also, d 2 V d x 2 < 0

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