I don't believe that an area/volume can change based on a change in shape

[Femme_physics]

And I know that I'm being extremely stupid in saying that.
I know I'm mathematically wrong.
Please convince me otherwise.

It doesn't make sense to me that if I change the shape of something it can alter its area/volume. I always thought these remain constant. Is there any experiment that I can see that will make me see the proof of it? Or a convincing argument without math, at least?

Seeing it mathematically is one thing, seeing it in reality is another.

 

[Doc Al]

It doesn't make sense to me that if I change the shape of something it can alter its area/volume.

What do you mean by 'something'? What are you keeping constant?

For a trivial example of how keeping the same volume but changing the shape can alter surface area: Imagine a ball of clay. Squash it into a flat pancake shape. By squashing it flat enough, you can make the surface area as much as you like.

You can do the same thing with a glass of water. In the glass, the water has some surface area. Spill it on the floor and the surface area is much more.

 

[Femme_physics]

What do you mean by 'something'? What are you keeping constant?

Any certain shape to another shape

What do you mean by 'something'? What are you keeping constant?

For a trivial example of how keeping the same volume but changing the shape can alter surface area: Imagine a ball of clay. Squash it into a flat pancake shape. By squashing it flat enough, you can make the surface area as much as you like.

You can do the same thing with a glass of water. In the glass, the water has some surface area. Spill it on the floor and the surface area is much more.

Ah, so the area is being lost to volume, and vice versa, yes? So we can say that these two have an inverse relationship?

Also, is a perfect ball the best shape for max volume?
Okay, I can understand "volume" and "area" relationship, but let's say I have a fence...how can I just by changing the way the fence is defined around the perimeter change the area. When it comes to area and volume, we can say that lost volume goes to area, and lost area goes to volume. Is there an inverse relationship in the fence example as well?

With fences, the length of the fence never changes, there's no volume in 2D, and yet somehow-- as though magically, the area size does!

 

[Pythagorean]

no volume is being lost. Surface area is being gained. In some geometric shapes you may say the effective thickness is being lost (like a cube gets flatter and flatter, losing thickness, gaining surface area)

You can also break things apart, like a snowball, and it now has more surface area, but same volume. I always kick snow all over during melt down to help the sun melt it faster by increasing the surface area [/nerd]

 

[Doc Al]

Any certain shape to another shape

That's too vague to be useful. Change a cube the size of your house to a sphere the size of a pea. Both volume and surface area have changed. So what? (In changing from one to the other something must be kept fixed.)

Ah, so the area is being lost to volume, and vice versa, yes? So we can say that these two have an inverse relationship?

No. As Pythagorean has pointed out, the volume remains fixed in those examples.

Also, is a perfect ball the best shape for max volume?

For a given surface area, yes.

Okay, I can understand "volume" and "area" relationship, but let's say I have a fence...how can I just by changing the way the fence is defined around the perimeter change the area. When it comes to area and volume, we can say that lost volume goes to area, and lost area goes to volume. Is there an inverse relationship in the fence example as well?

With fences, the length of the fence never changes, there's no volume in 2D, and yet somehow-- as though magically, the area size does!

I don't quite get what you're saying. In your fence example, the perimeter of the shape remains fixed (it equals the length of the fence). You can arrange the fence in a circle, a square, a thin rectangle; all have different areas, but the same perimeter.

 

[HallsofIvy]

Make a rectangle from four sticks, held together by pins so the sticks can pivot on the pins.

When the angles are right angles, so the figure is a rectangle, the area is largest. Now, warp the figure, pivoting on the pins, you can make the area smaller and smaller until, eventually, the area goes to 0.

You seem to believe there is some law of "conservation of area" or "conservation of volume" and that simply is not true.

 

[Femme_physics]

no volume is being lost. Surface area is being gained. In some geometric shapes you may say the effective thickness is being lost (like a cube gets flatter and flatter, losing thickness, gaining surface area)

Good point.

You can also break things apart, like a snowball, and it now has more surface area, but same volume. I always kick snow all over during melt down to help the sun melt it faster by increasing the surface area [/nerd]

Good Samaritan :)

I don't quite get what you're saying. In your fence example, the perimeter of the shape remains fixed (it equals the length of the fence). You can arrange the fence in a circle, a square, a thin rectangle; all have different areas, but the same perimeter.

Make a rectangle from four sticks, held together by pins so the sticks can pivot on the pins.

When the angles are right angles, so the figure is a rectangle, the area is largest. Now, warp the figure, pivoting on the pins, you can make the area smaller and smaller until, eventually, the area goes to 0.

You seem to believe there is some law of "conservation of area" or "conservation of volume" and that simply is not true.

It actually makes sense to me now that you explain how to get to area 0. I guess I can see now that such "law of conversation of area/volume" do not exist. It's just not intuitive to me. Or wasn't. I appreciate relating this to me :)

Thanks everyone, appreciate the feedback!

 

[Studiot]

no volume is being lost. Surface area is being gained.

Please note that this is not always true.

It is possible to reduce (or increase) the volume, whilst maintaing a constant surface area.

You can do this by exchanging a convex region of surface for a concave one and vice versa.

A simple example is a table tennis ball.

The whole surface is convex.

Press in a dimple with your finger, exactly the reverse to what was there before.

Voila (that's French)

Your ping pong ball now has the same surface area, but less volume.

go well

 

[I like Serena]

Here's another one.

When you crumple or flatten a milk carton or a coca cola can, the area remains the same, but the volume decreases.

 

[HallsofIvy]

Oh, I like that! Much more violent than my example!