A right triangle whose hypotenuse is \sqrt{3} m long is revolved about one of its legs to generate a right circular cone. The volume of the greatest cone in cu.m. made this way is

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Mathematics

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Question

A right triangle whose hypotenuse is $\sqrt{3}$ m long is revolved about one of its legs to generate a right circular cone. The volume of the greatest cone in cu.m. made this way is

none

$\frac{π}{3}$

$\frac{2 π}{3}$

2π

$V = \frac{1}{3} {πx}^{2} y and x^{2} + y^{2} = 3$
$V = \frac{1}{3} πy (3 - y^{2})$
$V^{'} (y) = \frac{π}{3} (3 - 3 y^{2}) = 0 \Rightarrow y = 1$

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