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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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The Aha! solution Comment 13 of 13 |

Since the radius (R) of the hole isn't given, it must be irrelevant to the solution, i.e., it can take any value in the range 0 to r.

Let's use R=0, in which case the "height" of the hole = diameter of the sphere => 2*r =4. So r = 2.

Therefore, the remaining  volume is just the volume of a sphere of radius 2 = 4/3* pi *2^3 = 32 * pi/3.

QED!   ;-)

  Posted by Jeff Kalwerisky on 2006-05-16 09:14:36
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