Volume and plane intersecting sphere

[FortranMan]

Homework Statement

A plane is tangent to the surface of a sphere. You then tilt the plane at an angle theta along one axis, causing it to begin passing through the sphere and splitting the sphere's volume into two regions. I claim the volume of the hemisphere the plane has just passed through is found from the equation below. How do I prove this using geometry?

Homework Equations

$$V = \frac{\pi R^{3}}{3}( cos^{3}(\theta) - 3 cos(\theta) + 2 )$$

The Attempt at a Solution

 

[ehild]

Attach a picture please, to show what theta is.

ehild

 

[Quinzio]

You prove it with integration of the sphere sections.
I'm not sure what d'you mean "geometrically".

 

[Brandon_R]

You prove it with integration of the sphere sections.
I'm not sure what d'you mean "geometrically".

I think he meant geometrically because he has not yet a working knowledge of calculus since this is in the precalculus section.