When you are dealing with volumes of solids obtained by rotation, you are dealing (in fact ) with functions symmetric with respect to the axis of rotation. It is possible to get zero if you were not accurate with plugging the limits of integration. You, probabaly, came up with two equal haves with opposite signs that cancel each other. Check for the limits when you were plugging your number b. I suspect, your integration (without plugging limits) was correct. But, any way, if you show the function to be integrated, we can be more specific in our recommendations. Good luck!
Probably, yes, though it's possible your teacher has given you a trick question! You should ALWAYS graph the shape you're rotating, either by using your graphing calculator or sketching on paper. Visualizing what you're doing clearly can help you avoid all sorts of problems. With these problems, easy mistakes to check for include switching the x and y axis, or rotating around the wrong line (for example, not all rotations go around the x or y axis). Check for these common mistakes, and if you're still having problems, post the actual question! Good luck!