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Area of circle<Area of circumference

Source: 2011 AMC A Problem 14

June 25, 2011
geometryprobabilityAMC

Problem Statement

A pair of standard 6-sided fair dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference?
<spanclass=′latex−bold′>(A)</span> 136<spanclass=′latex−bold′>(B)</span> 112<spanclass=′latex−bold′>(C)</span> 16<spanclass=′latex−bold′>(D)</span> 14<spanclass=′latex−bold′>(E)</span> 518<span class='latex-bold'>(A)</span>\,\frac{1}{36} \qquad<span class='latex-bold'>(B)</span>\,\frac{1}{12} \qquad<span class='latex-bold'>(C)</span>\,\frac{1}{6} \qquad<span class='latex-bold'>(D)</span>\,\frac{1}{4} \qquad<span class='latex-bold'>(E)</span>\,\frac{5}{18}
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