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The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is:
(1) $\sqrt{6}$
(2) $\frac{2}{3}\sqrt{3}$
(3) $2\sqrt{3}$
(4) $\sqrt{3}$
$r^2 + \frac{h^2}{4} = 9$. $V = \pi r^2 h = \pi h(9 - h^2/4)$. $\frac{dV}{dh} = \pi(9 - \frac{3h^2}{4}) = 0 \Rightarrow h = 2\sqrt{3}$.
BETA
