MathDB

14

Part of 2011 AMC 10

Problems(2)

Area of circle<Area of circumference

Source: 2011 AMC A Problem 14

6/25/2011
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}
geometryprobabilityAMC
Perimeter of parking lot

Source: AMC 10 2011 b Problem 14

2/24/2011
A rectangular parking lot has a diagonal of 2525 meters and an area of 168168 square meters. In meters, what is the perimeter of the parking lot?
<spanclass=′latex−bold′>(A)</span> 52<spanclass=′latex−bold′>(B)</span> 58<spanclass=′latex−bold′>(C)</span> 62<spanclass=′latex−bold′>(D)</span> 68<spanclass=′latex−bold′>(E)</span> 70 <span class='latex-bold'>(A)</span>\ 52 \qquad <span class='latex-bold'>(B)</span>\ 58 \qquad <span class='latex-bold'>(C)</span>\ 62 \qquad <span class='latex-bold'>(D)</span>\ 68 \qquad <span class='latex-bold'>(E)</span>\ 70
geometryperimeterrectanglenumber theoryPythagorean TheoremAMC