{"status": "success", "data": {"description_md": "Two right circular cylinders have the same volume. The radius of the second cylinder is $10\\%$ more than the radius of the first. What is the relationship between the heights of the two cylinders?\n\n$\\textbf{(A)}\\ \\text{The second height is } 10\\% \\text{ less than the first.} \\\\<br>\\qquad\\textbf{(B)}\\ \\text{The first height is } 10\\% \\text{ more than the second.} \\\\<br>\\qquad\\textbf{(C)}\\ \\text{The second height is } 21\\% \\text{ less than the first.} \\\\<br>\\qquad\\textbf{(D)}\\ \\text{The first height is } 21\\% \\text{ more than the second.} \\\\<br>\\qquad\\textbf{(E)}\\ \\text{The second height is } 80\\% \\text{ of the first.}$\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>Two right circular cylinders have the same volume. The radius of the second cylinder is  <span class=\"katex--inline\">10\\%</span>  more than the radius of the first. What is the relationship between the heights of the two cylinders?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\text{The second height is } 10\\% \\text{ less than the first.} \\\\\\qquad\\textbf{(B)}\\ \\text{The first height is } 10\\% \\text{ more than the second.} \\\\\\qquad\\textbf{(C)}\\ \\text{The second height is } 21\\% \\text{ less than the first.} \\\\\\qquad\\textbf{(D)}\\ \\text{The first height is } 21\\% \\text{ more than the second.} \\\\\\qquad\\textbf{(E)}\\ \\text{The second height is } 80\\% \\text{ of the first.}</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": "2015 AMC 12A Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12A_p08", "prev": "/problem/15_amc12A_p06"}}