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2014 AMC 10B Problem 23

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2014 AMC 10B Problem 23AMC 10 Step by Step
Name:                             Date: September 13, 2026
Solid Geometry · difficulty 5 of 5 · about 9 min · position P21-25

A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is twice that of the sphere. What is the ratio of the radius of the bottom base of the truncated cone to the radius of the top base of the truncated cone?

figure

  1. A)

    32\dfrac32

  2. B)

    1+52\dfrac{1+\sqrt5}2

  3. C)

    3\sqrt3

  4. D)

    22

  5. E)

    3+52\dfrac{3+\sqrt5}2

Working