Question

A round hole is drilled through the center of a spherical solid of radius r. The resulting cylindrical hole has a height of 4 cm.

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

b.) What is unusual about the answer?

Answer 1

I normally hate to just give the answer to problems, but this one was crazy.
I made an attempt at it, then started looking around on-line to find assistance.
This problem is considered a classic calculus problem. It comes up in numerous places on-line.
Rarely do they use calculus to solve it, which is a bummer since that is our main tool here.
The best solution that I found used mostly logic, splitting it into pieces and using geometry for each piece (one step to get a piece was blatantly not explained).
In the end, I think that I got the intended answer using calculus methods.

Answer 2

The "Classic Bead Problem."

Before I taught a calculus class, I saw a post on a teachers' website from a teacher who had casually assigned this problem to his class.

The next day the class was stumped, but when the teacher went to write the solution on the board, he was stumped, too.

Live and learn. You may learn from your mistakes, but it's better to learn from the mistakes of others!