Since the vertex angle of the cone is 60°, the cross-section triangle is
an equilateral triangle, with all sides equal in length, and each interior
angle equaling 60°.

The volume of the sphere is .
So we need only find the radius r and substitute.



Triangle AOB is a 30°-60°-90° right triangle, so the longer leg is √3 times
the shorter leg, so:



Square both sides:


Divide both sides by 3

Take positive square root of both sides:

Substitute 4 for r in



 cubic inches  <--Volume of the sphere.

Edwin