{"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": "<p>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$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "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"}}