ΒΆ 2012 AMC 10B Problem 17
Problem:
Jesse cuts a circular paper disk of radius along two radii to form two sectors, the smaller having a central angle of 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?
Answer Choices:
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B.
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E.
Solution:
Each sector forms a cone with slant height . The circumference of the base of the smaller cone is . Hence the radius of the base of the smaller cone is and its height is . Similarly, the circumference of the base of the larger cone is . Hence the radius of the base of the larger cone is and its height is . The ratio of the volume of the smaller cone to the volume of larger cone is
The problems on this page are the property of the MAA's American Mathematics Competitions