JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q74

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MathematicsSingle correct+4 / -1Question 74 of 90

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius $=\sqrt3$ is :

\dfrac43\sqrt3\,\pi

\dfrac83\sqrt3\,\pi

4\pi

2\pi

Answer and worked solution

Official answer: C

A cylinder in a sphere of radius $R$ with half-height $h$ has $V=2\pi h(R^2-h^2)$ . This is maximised at $h=\frac R{\sqrt3}$ , giving
$V_{\max}=\frac{4\pi R^3}{3\sqrt3}=\frac{4\pi\cdot3\sqrt3}{3\sqrt3}=4\pi.$

Topics:Maxima and minima

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 74