A round hole is drilled straight through the center of a solid metal sphere and out the other side. If the hole is exactly six inches in length, what is the volume of the remaining material?

Solution to Metal Sphere Puzzle

The key to solving this puzzle is to notice that there's apparently not enough data given. You're not told anything about the diameter of the sphere or the width of the hole, for example.

Since you're not told, assume it doesn't matter; compute the volume of a six-inch sphere with an infinitely thin hole through it using the standard formula (4/3)πr³, where r is the radius of the sphere, which is here 3 (because of the length of the hole through the diameter). This gives a result of 36π cubic inches.

Using more complex formulas you can prove that 36π is indeed the volume of the remaining material, no matter the size of the original sphere.

Remember, the hole must be exactly six inches long. If the sphere is as large as the sun, the hole would have be very wide indeed and the remaining strip of material very, very thin.