2014 AMC 12B Problems/Problem 19
Problem
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?
Solution
First, we draw the vertical cross-section passing through the middle of the frustum. let the top base equal 2 and the bottom base to be equal to 2r
then using the Pythagorean theorem we have: which is equivalent to: subtracting from both sides solving for s we get: next we can find the area of the frustum and of the sphere and we know so we can solve for using we get: using we get so we have: dividing by we get which is equivalent to so
See also
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 18 |
Followed by Problem 20 |
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All AMC 12 Problems and Solutions |
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