{"status": "success", "data": {"description_md": "A rectangular box $P$ is inscribed in a sphere of radius $r$. The surface area of $P$ is 384, and the sum of the lengths of its 12 edges is 112. What is $r$?\n\n$\\mathrm{(A) } 8 \\qquad \\mathrm{(B) } 10 \\qquad \\mathrm{(C) } 12 \\qquad \\mathrm{(D) } 14 \\qquad \\mathrm{(E) } 16$\n___\nFull 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>A rectangular box  <span class=\"katex--inline\">P</span>  is inscribed in a sphere of radius  <span class=\"katex--inline\">r</span> . The surface area of  <span class=\"katex--inline\">P</span>  is 384, and the sum of the lengths of its 12 edges is 112. What is  <span class=\"katex--inline\">r</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A) } 8 \\qquad \\mathrm{(B) } 10 \\qquad \\mathrm{(C) } 12 \\qquad \\mathrm{(D) } 14 \\qquad \\mathrm{(E) } 16</span> </p>&#10;<hr><p>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": "2005 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12A_p23", "prev": "/problem/05_amc12A_p21"}}