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Hole in a bead (Posted on 2004-08-21) Difficulty: 4 of 5
A round hole is drilled through the center of a spherical solid with a radius (r). The resulting cylindrical hole has height 4 cm.

a)What is the volume of the solid that remains?

b)What is unusual about the answer?

See The Solution Submitted by Pieater    
Rating: 3.0909 (11 votes)

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Solution Try This | Comment 10 of 13 |

a) Simply allow the hole to go to zero (imagine a sphere with a 4cm long hole of zero diameter drilled through the center) and compute the volume of a sphere with a diameter of 4cm, which gives 10 and 2/3 pi cubic centimeters as the volume remaining.

b) The solid remaining is constant regardless of the diameter of the hole or the size of the sphere. You will get the same result with a sphere the size of Mars.

Hugs. CeeAnne

  Posted by CeeAnne on 2004-10-22 07:31:07
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