Maybe this has already been posted. A friend asked me this a while back, and I answered her in less than a minute.

She said I was a genius. But I said there were two ways to arrive at the answer, and I simply chose the easier way.

A 6-inch [long] hole is drilled through a sphere.

What is the volume of the remaining portion of the sphere?

The hard way involves calculus. The easy way uses logic.

Quoting the original post, it says a 6 inch long hole,

*it doesn't specify the width.* I assume since it says 'through' the sphere, the hole must connect two outer edges of the sphere, be it straight through the center or off-centered or on a diagonal.

With only this information, I could theoretically get a drill bit whose diameter is the same as the sphere's diameter (or larger) and drill the sphere to nothingness no matter where the 6 inch long hole was drilled through it.

Google 'World's largest drill bit'. That would make a BIG difference compared to your standard hand held drill.