Coring the Sphere

Dec 01, 2021

It's time for the new puzzler. I already presented this puzzle as a challenge to our staff here at Car Talk Plaza. And  I'm going to use it because Doug Berman is still scratching his nose, trying to try to figure it out.

I think the question has to be very carefully worded.

You have a sphere, a solid sphere. And I don't want to tell you how big the sphere is because you have to figure that out. So you are going to drill through this to the center of this sphere with a tool, a drill. Or something like a drill, except the drill, is like a coring thing that you would core an apple with. A corer, if you will!

You are going to take this corer, and make a hole through the center of a sphere.

And the core is exactly six inches long. Or the corer is in fact a cylinder whose height is 6 inches.

So you're gonna push this cylinder through the sphere. Imagine if you were coring, let's say orange. So you're gonna push this thing through until the piece falls out the other end. Both the corer and the piece fall out.

Now the question is, how much of the material of the original sphere is left behind?

Now you'll notice I didn't fool around with any semantics or jargon. And I didn't obfuscate the puzzler, because I was remonstrated by everyone here, including especially Doug was said, this puzzler was lousy, and  that I should make it as clear, succinct, concise, uncomplicated, as possible.

And the question is, how much of the sphere remains after you take out the 6" core?



I have a semi answer to this puzzler that was the last one.

My biggest disappointment was that Doug Berman got the answer right away. I thought it was a good puzzle.

But if Doug gets the answer, then it's clear that was not a very challenging puzzle. Well, maybe I didn't stable may not realize that that you've heard of the organization called Mensa, which is for people with very, very high IQs. Well, Doug has just started an organization for automobile mechanics. He calls it Densa. He's the president.

So my brother figured out the answer, not even understanding the question, because of what was missing from the answer. He said, "since you did not specify the size of the sphere, that it must not make any difference. Therefore, I can make the sphere be any size I want it to be. It's right. And I chose to make it 6" in diameter."

Because we didn't specify what the diameter of the core was to be. We use limit theory. If it weren't for that, I would have no idea how to figure this out. Because if you use limit theory, and you shrink the diameter of the core down to zero, then the answer becomes four-thirds pi R cubed with R being three. And the answer becomes 36 pi units. Cubic inches, we said.

Pi R cubed, and you make R be whatever the heck you want it to be. In this case, the limit theory says it ought to be three.


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