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2020 AMC 12B Question 9

AMC12 · 2020 AMC 12B

Question 9

A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?

Question illustration
  1. $3\pi \sqrt{5}$
  2. $4\pi \sqrt{3}$
  3. $3\pi \sqrt{7}$
  4. $6\pi \sqrt{3}$
  5. $6\pi \sqrt{7}$