{"status": "success", "data": {"description_md": "A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?<br><center><img class=\"problem-image\" alt='[asy] draw(Arc((0,0), 4, 0, 270)); draw((0,-4)--(0,0)--(4,0)); label(\"$4$\", (2,0), S); [/asy]' class=\"latexcenter\" height=\"252\" src=\"https://latex.artofproblemsolving.com/0/f/d/0fd309aa42ba1222ee60252a6c9cb5860f74c4c4.png\" width=\"252\"/></center>\n\n$\\textbf{(A)}\\ 3\\pi \\sqrt5 \\qquad\\textbf{(B)}\\ 4\\pi \\sqrt3 \\qquad\\textbf{(C)}\\ 3 \\pi \\sqrt7 \\qquad\\textbf{(D)}\\ 6\\pi \\sqrt3 \\qquad\\textbf{(E)}\\ 6\\pi \\sqrt7$\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 three-quarter sector of a circle of radius  <span class=\"katex--inline\">4</span>  inches together with its interior can be rolled up to form the lateral surface of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?<br/><center><img class=\"latexcenter\" alt=\"[asy] draw(Arc((0,0), 4, 0, 270)); draw((0,-4)--(0,0)--(4,0)); label(&#34;$4$&#34;, (2,0), S); [/asy]\" height=\"252\" src=\"https://latex.artofproblemsolving.com/0/f/d/0fd309aa42ba1222ee60252a6c9cb5860f74c4c4.png\" width=\"252\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 3\\pi \\sqrt5 \\qquad\\textbf{(B)}\\ 4\\pi \\sqrt3 \\qquad\\textbf{(C)}\\ 3 \\pi \\sqrt7 \\qquad\\textbf{(D)}\\ 6\\pi \\sqrt3 \\qquad\\textbf{(E)}\\ 6\\pi \\sqrt7</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": 2, "problem_name": "2020 AMC 12B Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p10", "prev": "/problem/20_amc12B_p08"}}