MathDB
Paper Disk => Cones

Source: 2012 AMC 12 B #15

February 23, 2012
geometry3D geometryratioPythagorean TheoremAMC

Problem Statement

Jesse cuts a circular paper disk of radius 1212 along two radii to form two sectors, the smaller having a central angle of 120120 degrees. He makes two circular cones, using each sector to form the lateral surface of a cone. What is the ratio of the volume of the smaller cone to that of the larger?
<spanclass=latexbold>(A)</span> 18<spanclass=latexbold>(B)</span> 14<spanclass=latexbold>(C)</span> 1010<spanclass=latexbold>(D)</span> 56<spanclass=latexbold>(E)</span> 105 <span class='latex-bold'>(A)</span>\ \frac{1}{8} \qquad<span class='latex-bold'>(B)</span>\ \frac{1}{4} \qquad<span class='latex-bold'>(C)</span>\ \frac{\sqrt{10}}{10} \qquad<span class='latex-bold'>(D)</span>\ \frac{\sqrt{5}}{6} \qquad<span class='latex-bold'>(E)</span>\ \frac{\sqrt{10}}{5}