I'm kinda stuck on this.

I need to find the maximum size of a Cylinder that fits in sphere of radius 1.

Ive come up with the following, .. am I on the right track so far?

Volume of Cylinder = Pi(r^2)h = Pi(r^2)(sqrt(1^2 - r^2))

Volume of Sphere = 4/3(Pi)(r^3)

Pi(r^2)(sqrt(1^2 - r^2)) = 4/3(Pi)(r^3)

Now I just need to solve for r. Is this correct? Where does the differentiation come into it?