{"status": "success", "data": {"description_md": "Let $B$ be a right rectangular prism (box) with edges lengths $1,$ $3,$ and $4$, together with its interior. For real $r\\geq0$, let $S(r)$ be the set of points in $3$-dimensional space that lie within a distance $r$ of some point in $B$. The volume of $S(r)$ can be expressed as $ar^{3} + br^{2} + cr +d$, where $a,$ $b,$ $c,$ and $d$ are positive real numbers. What is $\\frac{bc}{ad}?$\n\n$\\textbf{(A) } 6 \\qquad\\textbf{(B) } 19 \\qquad\\textbf{(C) } 24 \\qquad\\textbf{(D) } 26 \\qquad\\textbf{(E) } 38$", "description_html": "

Let B be a right rectangular prism (box) with edges lengths 1, 3, and 4 , together with its interior. For real r\\geq0 , let S(r) be the set of points in 3 -dimensional space that lie within a distance r of some point in B . The volume of S(r) can be expressed as ar^{3} + br^{2} + cr +d , where a, b, c, and d are positive real numbers. What is \\frac{bc}{ad}?

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\\textbf{(A) } 6 \\qquad\\textbf{(B) } 19 \\qquad\\textbf{(C) } 24 \\qquad\\textbf{(D) } 26 \\qquad\\textbf{(E) } 38

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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": 3, "problem_name": "2020 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10B_p21", "prev": "/problem/20_amc10B_p19"}}