Finding largest volume of right circular cone inscribed in a sphere of radius 3

I would like some assistance solving the applied optimization problem in my my calculus book that ask that you find the largest volume for a right circular cone inscribed in a sphere of radius 3. The book provides an image
I would like some tips on where exactly I must start as I thought I had to solve for x then get y in terms of the radius r and then input that into my volume equation for the right circular cone then take the first derivative and solve for r to get the optimal value of r for the volume.

 

Start with what you know:

* the formula for the volume of a sphere
* the formula for the volume of a cone

From the picture:

* the radius of the base of the cone
* the expression for the height of the cone
* the radius of the sphere
* the Pythagorean Theorem

Use the Pythagorean Theorem to express y in terms of x. See where that leads....