tmua.me Medium Set E Paper 2 · Question 19

A sector of angle $\theta$ radians is removed from a circular sheet of radius $6\,\mathrm{cm}$ , where $0<\theta<2\pi$ . The straight edges of the remaining sector are joined, without overlap, to form the curved surface of a right circular cone.

What value of $\theta$ gives the greatest volume of the cone?

The volume of a cone of base radius $r$ and perpendicular height $h$ is $V=\frac13\pi r^2h$ .

2\pi\left(1-\dfrac1{\sqrt3}\right)

2\pi\sqrt{\dfrac23}

2\pi\left(1-\sqrt{\dfrac23}\right)

\pi\left(1-\sqrt{\dfrac23}\right)

2\pi\left(1-\dfrac1{\sqrt2}\right)

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tmua.me Medium Set E Paper 2 · Q19