A circular cylinder is inscribed in a right circular cone of base radius $2c$ and vertical height $c

Question

A circular cylinder is inscribed in a right circular cone of base radius $2c$ and vertical height $c$. One of the circular ends of the cylinder lies on the base of the cone and the other end is in contact with the inner surface of the cone. If the cylinder has base radius $x$, find the expressions for the volume $V$ and the total surface area $S$ of the cylinder in terms of $c$ and $x$. If $c$is fixed and $x$ varies, find the maximum value of $V$.[8]

Prove that $S$ cannot exceed $8\pi {{c}^{2}}$.[2]

Accepted Answer

$V_{max}=\frac{16}{27}\pi c^3$; $S\le8\pi c^2$

2010 NYJC P2 Q2

2010 NYJC P2 Q2

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