{"status": "success", "data": {"description_md": "Corners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?<br>\t\n\n$\\mathrm{(A)}\\ \\frac{5\\sqrt{2}-7}{3}\\qquad \\mathrm{(B)}\\ \\frac{10-7\\sqrt{2}}{3}\\qquad \\mathrm{(C)}\\ \\frac{3-2\\sqrt{2}}{3}\\qquad \\mathrm{(D)}\\ \\frac{8\\sqrt{2}-11}{3}\\qquad \\mathrm{(E)}\\ \\frac{6-4\\sqrt{2}}{3}$\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>Corners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?<br/></p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{5\\sqrt{2}-7}{3}\\qquad \\mathrm{(B)}\\ \\frac{10-7\\sqrt{2}}{3}\\qquad \\mathrm{(C)}\\ \\frac{3-2\\sqrt{2}}{3}\\qquad \\mathrm{(D)}\\ \\frac{8\\sqrt{2}-11}{3}\\qquad \\mathrm{(E)}\\ \\frac{6-4\\sqrt{2}}{3}</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2007 AMC 12A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p21", "prev": "/problem/07_amc12A_p19"}}