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

A right circular cylinder, 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).


Refer to the figure below.


By ratio and proportion of two similar triangles ΔBCD and ΔACE, we have

\displaystyle \frac{y}{r-x}=\frac{h}{r}

\displaystyle y=\frac{h\left(r-x\right)\:}{r}