2014 AMC 12B Problems/Problem 19
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 (diagram by DivideBy0?)
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