Here's another challenge problem if anyone would like a go.

Please excuse my hackneyed paint drawing. I hope it's OK.

"A wedge is cut from a right circular cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle @ with the first. Find the volume of the wedge by slicing perpendicular to the y-axis. Try it perp. to the x-axis."

I get: V= \frac 2 3 R^3 tan(\theta).

Slicing perpendicular to y-axis gives:


V = \int_0 ^R (R^2-x^2)tan(\theta) dx.


Slicing perpendicular to x-axis gives:


V = 2 \int _0 ^R x tan(\theta) \sqrt{R^2-x^2} dx

That was too easy. I knew you'd get it, ebaines.:cool: I will have to think of something a little more challenging. Something along the lines of number theory? :)

Galactus: I'll post one for you - the classic "bug problem."