1987 AHSME Problems/Problem 22
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 as the top and cm deep. What was the radius of the ball (in centimeters)?
Solution
Consider a cross-section of this problem in which a circle lies with its center somewhere above a line. A line segment of cm can be drawn from the line to the bottom of the ball. Denote the distance between the center of the circle and the line as . We can construct a right triangle by dragging the center of the circle to the intersection of the circle and the line. We then have the equation , . Solving, the answer is .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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