Suppose we want to form a conic container by rolling up a circular sector of radius 10. We want to find the central angle (theta) such that it maximizes the volume of the cone. Find the radius and the...

Suppose we want to form a conic container by rolling up a circular sector of radius 10.

We want to find the central angle (theta) such that it maximizes the volume of the cone.

Find the radius and the height of the cone and then express the volume as a function of theta. Make sure you state the domain.