I found this puzzle here. (It's labeled "crossed cylinders".) Here's the description:
Two cylinders of equal radius are intersected at right angles as shown at left. Find the volume of the intersection between the two cylinders, without using calculus! A 3D picture of the intersection is shown at right.
Hint (medium hint - exactly which high school formulae you need): 1) Area of circle = pi * radius2, and 2) Volume of sphere = (4/3) * pi * radius3
Note: Solved by the mathematician Archimedes (287 B.C. - 212 B.C.), waaay before calculus came around!!
Please tell me how to solve this puzzle! Is there a way to do this without setting up a Riemann sum and finding a limit, essentially evaluating an integral?