### Brain Teasers

# Doughnut Hole

If a solid piece of iron shaped as a doughnut was placed under extreme heat, what would the hole in the middle do?

### Answer

It would grow larger.Hide Answer Show Answer

## What Next?

View a Similar Brain Teaser...

If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.

### Solve a Puzzle

## Comments

The hole would do nothing. The metal would change thereby having an effect on the hole. 'What would happen to the hole' might be better wording. I did, however, approach this as if it contained a trick.

The problem with this is: "Extreme heat"!

The answer is correct until you reach the melting point!

After that, you just have a pot of melted steel!

JR

The answer is correct until you reach the melting point!

After that, you just have a pot of melted steel!

JR

Even if you are saying that as the metal heats up it expands, remember it will expand in all directions. This includes inward.

I think that I can explain this. For every degree that a metal is heated, it will expand in all directions by a certain percent (depending on the metal). Lets say that this metal expands by 10% for each degree.

(a) If metal in the shape of a donut expands, the circumference will increase by 10%. This will increase the radius by 10%.

(b) At the same time, the thickness of the ring will increase by 10%. This will decrease the radius by 10% X (the ring thickness) X 1/2. This number is smaller that the number in part (a). Therefore, the hole expands.

It's easier to visualize if you picture something bigger and thinner, like a magician's ring. If you heat it up, the diameter of the ring will grow quite a bit, but it will not get much thicker.

(a) If metal in the shape of a donut expands, the circumference will increase by 10%. This will increase the radius by 10%.

(b) At the same time, the thickness of the ring will increase by 10%. This will decrease the radius by 10% X (the ring thickness) X 1/2. This number is smaller that the number in part (a). Therefore, the hole expands.

It's easier to visualize if you picture something bigger and thinner, like a magician's ring. If you heat it up, the diameter of the ring will grow quite a bit, but it will not get much thicker.

I'm inclined to agree with captbob

Dearest Captbob and Jim. As a man of science, I would like to state here and now that the two of you are both dead wrong. I tried to explain it to you in reasonably simple terms, but apparently that was not enough (I will admit that it is tough to explain, however). So for the two of you, I will ask you to just go on faith - THE HOLE EXPANDS. PERIOD.

I agree with jeanray on this one. I was thinking extreme heat was melting the metal and then the hole would fill in. Rewording the teaser to heating it just under the melting point or something like that would be much better.

Once again I find Bobbrt's comments far more enlightening than the original explanation. I appreciate the explanation. Of course I already knew the answer because plumbers and mechanics heat a metal joint to sweat one pipe of another. Heating a pipe clearly enalrges the hole or else they would frezze it to get it off. Thanks for the interesting teaser and thanks Bob for the explanation.

definitely the hole expands...

Here, all I know is that the hole will expand, as Bob have explained. It also will expand in an inward direction, however, this will not make the radius go smaller, but will contribute to its expansion...

Thank you Bobbrt for that explanation. I was confused but after seeing that I'm kicking myself in the bum. The same thing is used in auto mechanics to get off old hoses and piping.

It helps me to visualize it by imagining that there is a metal torus, within which there exists a cylinder barely smaller than the hole. Assuming the coefficient of thermal expansion are identical, the ring and the piece in the hole would grow proportionally as if it were a single cylinder. One can then remove the center piece. The result is the same. An extension of this property explains why running a glass jar with a metal lid (greater coefficient of thermal expansion than glass) under hot water makes it easier to open. At my college, we played with a metal ring and metal ball. Initially, the ball fits through the ring. Then the sphere is subjected to a bunson burner or other heat source. The ball is then too large to fit through the ring... That is, until the ring is heated as well.

To post a comment, please create an account and sign in.

## Follow Braingle!