Ok, this problem is killing me, can I get some help?

Find the volume of the largest(maximize) right circular cone that can be inscribed in a sphere of radius 4.

So, so far ive gotten $\displaystyle x^2 + y^2 = 4^2$ so $\displaystyle y^2 = 4^2 + x^2$ the $\displaystyle y= sqrroot 16-x^2$ and therfore $\displaystyle h=4+y$ so $\displaystyle h=4+ sqrroot 16-x^2$

Am I going in the right direction?

Thanks!!