Problem 1
A ball was floating in the lake when the lake froze. The ball was removed (without breaking the ice), leaving a hole 24cm across at the top and 8cm deep. What was the radius of the ball (in centimeters)?
Solution
In the figure, we show a cross section of the ball still in the ice. Since angle OCA = 90 degrees,
(r-8)*(r-8) + 12*12 = r*r
Solving, one finds r = (64 + 144)/ 16 = 13
