{"status": "success", "data": {"description_md": "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 $m + n + p$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2010 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_I_p12", "prev": "/problem/10_aime_I_p10"}}