Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 7

A right circular cylinder, a radius of base $x$ , height $y$ , is inscribed in a right circular cone, radius of base $r$ and a height $h$ . Express $y$ as a function of $x$ ( $r$ and $h$ are constants).

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SOLUTION:

Refer to the figure below for an elevation view.

By ratio and proportion of two similar triangles, we have

\begin{align*} \frac{y}{r-x} & = \frac{h}{r} \\ y & =\frac{h\left(r-x\right)\:}{r} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \\ \end{align*}