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2012 AMC 12B Question 15

AMC12 · 2012 AMC 12B

Question 15

Jesse cuts a circular paper disk of radius $12$ along two radii to form two sectors, the smaller having a central angle of $120$ 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?
  1. $\dfrac{1}{8}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{\sqrt{10}}{10}$
  4. $\dfrac{\sqrt{5}}{6}$
  5. $\dfrac{\sqrt{10}}{5}$