{"status": "success", "data": {"description_md": "<center>\n<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/6/6/d/66db58ca0de01a6dab5b8ddb18e671f265759bfa.png\" width=\"202\"/>\n</center><br>\n\nRolly wishes to secure his dog with an $8$-foot rope to a square shed that is $16$ feet on each side. His preliminary drawings are shown. Which of these arrangements give the dog the greater area to roam, and by how many square feet?\n\n$\\mathrm{(A)}\\ \\text{I, by}\\ 8\\pi\\qquad\\mathrm{(B)}\\ \\text{I, by}\\ 6\\pi\\qquad\\mathrm{(C)}\\ \\text{II, by}\\ 4\\pi\\qquad\\mathrm{(D)} \\text{II, by}\\ 8\\pi\\qquad\\mathrm{(E)}\\ \\text{II, by}\\ 10\\pi$", "description_html": "<center>&#10;<img class=\"problem-image\" height=\"252\" src=\"https://latex.artofproblemsolving.com/6/6/d/66db58ca0de01a6dab5b8ddb18e671f265759bfa.png\" width=\"202\"/>&#10;</center><br/>&#10;<p>Rolly wishes to secure his dog with an <span class=\"katex--inline\">8</span>-foot rope to a square shed that is <span class=\"katex--inline\">16</span> feet on each side. His preliminary drawings are shown. Which of these arrangements give the dog the greater area to roam, and by how many square feet?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\text{I, by}\\ 8\\pi\\qquad\\mathrm{(B)}\\ \\text{I, by}\\ 6\\pi\\qquad\\mathrm{(C)}\\ \\text{II, by}\\ 4\\pi\\qquad\\mathrm{(D)} \\text{II, by}\\ 8\\pi\\qquad\\mathrm{(E)}\\ \\text{II, by}\\ 10\\pi</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2006 AMC 10A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10A_p13", "prev": "/problem/06_amc10A_p11"}}