Finding the dimensions of the the right circular cylinder of greatest volume Find the dimensions of the the right circular cylinder of greatest volume
that can be inscribed in a given right circular cone with radius $b$ and
height $a$.  The figure
I have tried to do $V=\pi r^2h$ but how to make $V$ a function of one variable using the cone dimensions?

Hint...use similar triangles $$\frac{a-h}{r}=\frac ab$$ to eliminate either $r$ or $h$ so you have a function of one variable.
