{"status": "success", "data": {"description_md": "A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top $\\frac{1}{8}$ of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet?\n\n$\\textbf{(A)}\\ 4000 \\qquad \\textbf{(B)}\\ 2000(4-\\sqrt{2}) \\qquad \\textbf{(C)}\\ 6000 \\qquad \\textbf{(D)}\\ 6400 \\qquad \\textbf{(E)}\\ 7000$\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 cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top  <span class=\"katex--inline\">\\frac{1}{8}</span>  of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 4000 \\qquad \\textbf{(B)}\\ 2000(4-\\sqrt{2}) \\qquad \\textbf{(C)}\\ 6000 \\qquad \\textbf{(D)}\\ 6400 \\qquad \\textbf{(E)}\\ 7000</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": "2008 AMC 12B Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12B_p12", "prev": "/problem/08_amc12B_p10"}}