Find the circular cone of maximum volume inscribed in a sphere of radius a.

I can visualize what the problem is trying to say, but the problem is..I don't know the solution :( Help

-thank you

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- Nov 12th 2008, 07:53 AMihmthmaximum volume
Find the circular cone of maximum volume inscribed in a sphere of radius a.

I can visualize what the problem is trying to say, but the problem is..I don't know the solution :( Help

-thank you - Nov 12th 2008, 08:12 AMearboth
I've attached a sketch of the situation.

1. You are dealing with a right triangle. According to Euklids theorem you have:

and :

2. The volume of the cone is calculated by:

3. Substitute :

and

4. You have now the volume as a function of h:

5. Calculate the first derivation of V(h) and solve V'(h) = 0 for h.

I've got