Okay. So this isn't geometry; it's calculus. And you're not doing anything standard like finding the volume of a cylinder in a nice orientation; you're finding the partial volume of a complicated shape in a not-nice orientation. That was important information. (Admin/mods: Please move this to "calculus".)
You can see lots of Q-and-A's on the Ask Dr. Math
site. There's a long discussion with two worked examples in this article
. And you may be able to check your work by using this calculator
. If you get stuck, please write back showing what you've done so far. Thanks.