Question

find the volume of the largest right circular cone that can be inscribed in a sphere of radius a

Answer 1

You might benefit from drawing this situation. If you cut both cone and sphere vertically right down the middle, you'll obtain a drawing like this:

Answer 2

Label all relevant quantities, such as the height of the cone, the radius or the diameter of the base of the cone, and so on. Think: What is/are the relationship(s) between these several variables (except that 'a' is not a variable, but a constant)?

You are to maximize the volume of the cone. Which tools of mathematics / calculus are appropriate for that task?

Answer 3

http://mathforum.org/library/drmath/view/53493.html