{"status": "success", "data": {"description_md": "Rhombus $ABCD$, with side length $6$, is rolled to form a cylinder of volume $6$ by taping $\\overline{AB}$ to $\\overline{DC}$. What is $\\sin(\\angle ABC)$?\n\n$\\mathrm {(A)} \\frac{\\pi}{9}\\qquad \\mathrm {(B)} \\frac{1}{2}\\qquad \\mathrm {(C)} \\frac{\\pi}{6}\\qquad \\mathrm {(D)} \\frac{\\pi}{4}\\qquad \\mathrm {(E)} \\frac{\\sqrt{3}}{2}$\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>Rhombus  <span class=\"katex--inline\">ABCD</span> , with side length  <span class=\"katex--inline\">6</span> , is rolled to form a cylinder of volume  <span class=\"katex--inline\">6</span>  by taping  <span class=\"katex--inline\">\\overline{AB}</span>  to  <span class=\"katex--inline\">\\overline{DC}</span> . What is  <span class=\"katex--inline\">\\sin(\\angle ABC)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} \\frac{\\pi}{9}\\qquad \\mathrm {(B)} \\frac{1}{2}\\qquad \\mathrm {(C)} \\frac{\\pi}{6}\\qquad \\mathrm {(D)} \\frac{\\pi}{4}\\qquad \\mathrm {(E)} \\frac{\\sqrt{3}}{2}</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": 3, "problem_name": "2007 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p20", "prev": "/problem/07_amc12B_p18"}}