Here's a cool calc problem you may wish to tackle. Perhaps you've seen it before.

"A wedge is cut from a 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 wegde by slicing perpendicular to the y-axis".

Then find the volume by slicing perpendicular to the x-axis.

Here's a diagram to help. I used @ instead of theta because I used paint to construct the diagram.