Comparing Volume of Oval vs Circle: Joe's First Post

In summary, the volume of a 4 inch round pipe changes when it is made oval-shaped by inserting it into a vice, as demonstrated in a video on a drag racing forum. The crushing and distortion of the pipe make it difficult to accurately measure the change in volume, but it is confirmed that the volume does decrease. The isoperimetric inequality provides the best explanation for this change.
  • #1
turbojoe
2
0
This is my first post here and any help is appreciated. I belong to a drag racing forum and
this has been a hot topic of discussion.

If you have a 4 inch round pipe by 2 inches tall and insert the pipe into a vice and make it oval shaped it would somehow change the volume.

Please see video below.

http://www.youtube.com/watch?v=B24PtgujPOo&feature=youtu.be

thread from racing forum.

http://www.yellowbullet.com/forum/showthread.php?t=435379

I was under the assumption that the volume would not change. I suppose I'm wrong.

TIA,
Joe
 
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  • #2
The volume does change, this can be seen from the limit case that the pipe is crushed flat. If crushed flat enough, there is no volume left inside the pipe. However, to know how much the volume has changed at any instant before this limit case, well, that's a little more difficult. The crushing of the pipe distorts it irregularly and creates some kinks as well. It is very hard to model a situation like that exactly. To me, it seems hard to choose a best fitting ellipse to model the shape he has in the video. I'm not sure if you were looking for how to measure the volume directly (using integrals) or if you just wanted to know for sure if the volume does, in fact, decrease. Well it does (Technically the volume is infinite as the solid is not a closed one, one has to restrict the cylinder with two planes).
 
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  • #3
thanks for your response.. isoperimetric inequality seems to be the best explanation
 

FAQ: Comparing Volume of Oval vs Circle: Joe's First Post

What is the difference between the volume of an oval and a circle?

The main difference between the volume of an oval and a circle is the shape. A circle is a two-dimensional shape with a constant radius, while an oval is a three-dimensional shape with varying radii. This means that the volume of an oval will always be greater than the volume of a circle with the same radius.

How do you calculate the volume of an oval and a circle?

The formula for calculating the volume of a circle is V = πr^2h, where r is the radius and h is the height. The formula for calculating the volume of an oval is V = πr1r2h, where r1 and r2 are the radii of the oval and h is the height. Essentially, the volume of an oval is calculated by multiplying the volume of a circle with the average of its two radii.

Which shape has a greater volume, an oval or a circle with the same radius?

An oval will always have a greater volume than a circle with the same radius. This is because an oval has a larger surface area, and therefore, more space to contain the volume.

Is there a specific scenario where the volume of a circle and an oval would be the same?

No, there is no scenario where the volume of a circle and an oval would be the same, unless the oval is a perfect circle. In that case, the two shapes would have the same volume.

How does the volume of an oval and a circle change as their radii increase?

The volume of both an oval and a circle increases as their radii increase. However, the volume of an oval increases at a faster rate compared to a circle, as it has a larger surface area. This means that the larger the radii of the oval and circle, the greater the difference in their volumes will be.

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