Thread: maximum 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

Originally Posted by ihmth

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

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