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A paper drinking cup filled with water has the shape of a cone with height h and
semi-vertical angle 0 (see figure). A ball is placed carefully in the cup, thereby
displacing some of the water and making it overflow. What is the radius of the ball
that causes the greatest volume of water to spill out of the cup?
h
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A paper drinking cup filled with water has the shape of a cone with height h and semi-vertical angle 0 (see figure). A ball is placed carefully in the cup, thereby displacing some of the water and making it overflow. What is the radius of the ball that causes the greatest volume of water to spill out of the cup? h

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