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What is the formula for calculating the volume of a sphere that has had a cylinder removed? |
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Napkin Ring Problem
Although you said "cylinder," if you drill a hole through the center of a sphere, the shape of the volume you drill out is not a perfect cylinder. It looks more like a medicine capsule, a cylinder with convex end caps.
The volume of a sphere = (4/3)*pi*r3, and the volume of a cylinder = pi*r2*h, where r is the radius and h is the height.
So, the volume you're looking for is the volume of the sphere minus the volume of the cylinder minus the volume of the two end caps = (4/3)*pi*r3 - pi*r2*h - volume of the end caps. It requires calculus to determine the volume of the end caps.
Keith Devlin of the Mathematical Association of America provides an outstanding explanation of this problem, including the computation of the end caps. See the nearby link.
First answer by Peterfromredcar. Last edit by Schnazola. Contributor trust: 1304 [recommend contributor]. Question popularity: 8 [recommend question]
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