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2012 AMC 10B Question 17

AMC10 · 2012 AMC 10B

Question 17

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} $