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Question

A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three holes are drilled in the ball. Bowler Kris has holes drilled that are 8 cm deep and have diameters of 2 cm, 2 cm, and 3 cm. Assuming the three holes are right circular cylinders, find the number of cubic centimeters in the volume of the fitted bowling ball. Express your answer in terms of .

Accepted Answer

The untampered bowling ball has radius 30/2=15 cm and volume 43(15^3)=4 15^2 5=225 20 = 4500 cubic cm. The 2 cm cylindrical holes each have radius 2/2=1 cm and volume (1^2)(8)=8 cubic cm; the 3 cm cylindrical hole has radius 3/2 cm and volume (32)^2(8)=9 2 = 18 cubic cm. Post hole-removal the fitted ball has volume 4500 - 2 8 - 18 = 4466 cubic cm.