What is the optimal angle for a conical cup with a maximum volume?

[cateater2000]

A conical cup is to be made by joining the edges OA, OB of the sector of a circle of radius 8cm. What angle @ gives the cup of maximum volume?


I'm having trouble solving this question. This is what I have done so far

we know V=pi*r^2*h/3

r is given, so we need to put h in terms of @.
now by similar triangles we can take another slice, and compare
r/h=R/(h-1)... (h-1) is just the height of the triangle below the new slice
solving for h I get h=1/(1-R/r) now I'm unsure of what to do now, and how to get @ into the equation.


Anyways please let me know if I'm doing this question completely wrong or what not. Thanks for all your help

 

[Tide]

r is not given! You're given the radius of the sector of the circle but that is not the same as the radius of the cone.

 

[Phymath]

a picture would help