Problem:
A ball was floating in a lake when the lake froze. The ball was removed (without breaking the ice), leaving a hole cm across at the top and cm deep. What was the radius of the ball (in centimeters)?
Answer Choices:
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Solution:
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In the figure, we show a cross section of the ball still in the ice. Since .
Solving, one finds
Query. We have assumed the ball floated with its center above the water, for otherwise the ball could not be removed without breaking the ice. Is there a second mathematical solution with the center below the water line?