Applications of Integration · Superchallenge problem

A solid extends from $x=0$ to $x=h$. Its cross-section perpendicular to the $x$-axis at position $x$ is an ellipse with semi-axes $x$ and $h-x$ (so the ellipse degenerates to a point at both ends). For what value of $h>0$ is the solid's volume exactly $36\pi$?