{"status": "success", "data": {"description_md": "A cylindrical barrel with radius $4$ feet and height $10$ feet is full of water. A solid cube with side length $8$ feet is set into the barrel so that the diagonal of the cube is vertical. The volume of water thus displaced is $v$ cubic feet. Find $v^2$.<br><br>$\\includegraphics[width=69, height=119, totalheight=119]{https://latex.artofproblemsolving.com/7/5/d/75de39adfa735e8d8b65a77fa6a8807ba3f4bef1.png}$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 cylindrical barrel with radius <span class=\"katex--inline\">4</span> feet and height <span class=\"katex--inline\">10</span> feet is full of water. A solid cube with side length <span class=\"katex--inline\">8</span> feet is set into the barrel so that the diagonal of the cube is vertical. The volume of water thus displaced is <span class=\"katex--inline\">v</span> cubic feet. Find <span class=\"katex--inline\">v^2</span>.<br/><br/><img src=\"https://latex.artofproblemsolving.com/7/5/d/75de39adfa735e8d8b65a77fa6a8807ba3f4bef1.png\" width=\"69\" height=\"119\" class=\"problem-image\"/></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 4, "problem_name": "2015 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_II_p10", "prev": "/problem/15_aime_II_p08"}}