2010 AIME I Problem 11

Let \mathcal{R} be the region consisting of the set of points in the coordinate plane that satisfy both |8 - x| + y \le 10 and 3y - x \ge 15. When \mathcal{R} is revolved around the line whose equation is 3y - x = 15, the volume of the resulting solid is \frac {m\pi}{n\sqrt {p}}, where m, n, and p are positive integers, m and n are relatively prime, and p is not divisible by the square of any prime. Find m + n + p.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.