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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.

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.