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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 Clever problem. | Comment 4 of 13 |

a) If a is the radius of the drilled hole, then r^2 = a^2 + 2^2. If we let a -> 0, then r -> 2. Therefore, the volume of solid that remains is (4/3)*נ*r^3 or 32*נ/3 cm^3.

b) The answer is independent of the radius r. Although r must be greater than 2.

  Posted by Bractals on 2004-08-21 10:00:48
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