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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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Some Thoughts Pythagorean Theorem | Comment 8 of 13 |
I think nikki nailed it. At first glance, I thought that the missing radius of the hole would be needed for a solution.

I find it interesting that the Pythagoren Theorem allows us to express the radius of the hole in terms of the given height of the hole and the radius of the sphere.

What blows my mind is that in working the equations to find the remaining volume, all of the radius terms cancel out, leaving only the simple formula based only on the given hole height.

I can see and follow nikki's solution, but a part of me still doesn't want to believe it.

  Posted by Bob Marsh on 2004-08-24 03:55:29
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