Thanks for all the fun entries! The past few weeks have been entertaining, to say the least.

I saved one of my favorites, and one of the more tricky problems, for last. It’s not the simplest to set up mathematically, but can be solved intuitively.

Last week’s problem:

Hole in the Sphere

A cylindrical hole 6-inches long has been drilled straight through the center of a solid sphere. What is the volume remaining in the sphere?

I picked at random this week, and Don nailed it with his simple explanation.

The problem doesn’t state the width of the cylindrical hole. Therefore, if the problem has a unique solution, the answer must be independent of the hole’s width.

Therefore, we can safely assume a limiting case, that the width of the hole is zero. In this case the ‘remaining’ volume is simply the entire volume of a sphere three inches in radius: that is to say, 4/3 * pi * 3^3, or simplifying, 36*pi cubic inches.

I ran these contests as a way to launch the book here at our blog; when I started we just had some pre-release copies sitting around. It’s out now, and available nation-wide.

For previous contest entries too entertaining to tuck away in my inbox, see the Hall of Fame.