gluPerspective() question

How do I know what the size of my viewing volume is after using gluPerspective() to create my viewing volume?

The very first value you pass to gluPerspective is the angle of the viewing frustrum. From there you can work out the volume…

… and you can compute the volume from the projection matrix alone.

Any point that maps to +/-1 x/y and 0…1 z is visible. You just need to exploit these constraints by fittings planes through the set of points on the boundary.