



 
Hi, In my diagram the sphere has centre C and radius R. The cone has base radius r and height h.
The volume of a right circular cone is V = 1/3 π r^{2 }h. To apply the calculus you know you need to express this volume as a function of one variable. The right triangle ABC give the information you need. By Pythagoras theorem
thus
or
Substitute r^{2} into the expression for the volume of the cone and you have then a function of one variable h. Use your calculus to find the value of h that maximized the volume. Harley  


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