{"status": "success", "data": {"description_md": "A lampshade is made in the form of the lateral surface of the frustum of a right circular cone. The height of the frustum is $3\\sqrt3$ inches, its top diameter is $6$ inches, and its bottom diameter is $12$ inches. A bug is at the bottom of the lampshade and there is a glob of honey on the top edge of the lampshade at the spot farthest from the bug. The bug wants to crawl to the honey, but it must stay on the surface of the lampshade. What is the length in inches of its shortest path to the honey?\n\n$\\textbf{(A) } 6 + 3\\pi\\qquad \\textbf{(B) }6 + 6\\pi\\qquad \\textbf{(C) } 6\\sqrt3 \\qquad \\textbf{(D) } 6\\sqrt5 \\qquad \\textbf{(E) } 6\\sqrt3 + \\pi$\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 lampshade is made in the form of the lateral surface of the frustum of a right circular cone. The height of the frustum is  <span class=\"katex--inline\">3\\sqrt3</span>  inches, its top diameter is  <span class=\"katex--inline\">6</span>  inches, and its bottom diameter is  <span class=\"katex--inline\">12</span>  inches. A bug is at the bottom of the lampshade and there is a glob of honey on the top edge of the lampshade at the spot farthest from the bug. The bug wants to crawl to the honey, but it must stay on the surface of the lampshade. What is the length in inches of its shortest path to the honey?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 6 + 3\\pi\\qquad \\textbf{(B) }6 + 6\\pi\\qquad \\textbf{(C) } 6\\sqrt3 \\qquad \\textbf{(D) } 6\\sqrt5 \\qquad \\textbf{(E) } 6\\sqrt3 + \\pi</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": "2023 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p22", "prev": "/problem/23_amc12B_p20"}}