Atmospheric pressure per square cm

[Theg]

Hi, I have a problem to understand one small thing. They say that air pressure per square cm at sea level is approximately 1 kg.
So at 2 sq cm it will be 2 kg, at 3 sq cm it will be 3 kg etc.
But... Here where I have a problem. The thing is that inside 2 square cm you can put 4 one square cm. Inside 3 square cm you can put nine square cm.
Just look at it this way:
2sq= 4= 1sq+1sq+1sq+1sq
3sq= 9 =
1sq+1sq+1sq+1sq+1sq+1sq+1sq+1sq+1sq
You see? So according to this logic the air pressure supposed to grow exponentially when you increase the surface, but according to textbooks it's not. Why?
It's supposed to be 1 kg at 1 sq cm, 4 kg at 2 sq cm, 9 kg at 3 cm etc.
See my trouble?

 

[gmax137]

Denoting pressures in units of kg/cm^2 is done but it is sloppy; use Pascals (N/m^2) instead.

Your confusion over area is not uncommon, people say "two centimeters square" meaning, a square with sides of length 2 cm. This has an area of four square centimeters (4 cm^2). An area of 2 cm^2 would be a square with sides of length 1.414 cm (because 1.414 * 1.414 = 2).

 

[gmax137]

Pressures in units of kg/cm^2 is sloppy because it assumes you are located somewhere (like the surface of the earth) where gravitational acceleration is 9.8 m/sec^2

 

[Theg]

Denoting pressures in units of kg/cm^2 is done but it is sloppy; use Pascals (N/m^2) instead.

Your confusion over area is not uncommon, people say "two centimeters square" meaning, a square with sides of length 2 cm. This has an area of four square centimeters (4 cm^2). An area of 2 cm^2 would be a square with sides of length 1.414 cm (because 1.414 * 1.414 = 2).

Ohh so you say my mistake is how I calculate square area? So an area of 2cm^2 isn't equale to a square with sides of length 2 cm?

 

[gmax137]

an area of 2cm^2 isn't equale to a square with sides of length 2 cm?

Correct. As you said in your first post, a square with sides of length 2 cm has an area of 4 cm^2.

There is a difference in the written words:
"an area of (two cm), squared"
"an area of two (cm squared)"

Confusing? Yes. This is a problem with English, I don't know if other languages are also ambiguous in this way.

 

[sophiecentaur]

In the past we used to say "two square cms" and the convention still applies when we buy carpet or tiles in square metres. Using "two cm²" took its place in Science and I am not sure it helped at all.

 

[phyzguy]

By the way, one complaint (sorry to nitpick, but this is a pet peeve of mine). If something grows as the square (i.e. 1 kg for a 1 cm square, 4 kg for a 2 cm square, 9kg for a 3 cm square...), this is growing quadratically, not exponentially. It has become common practice for people to describe anything that grows faster than linear as "exponential". Exponential growth is faster than any power (faster than x^2, faster than x^3, faster than x^4...).

It turns out I'm not the only one that is bothered by this:

https://www.nytimes.com/2019/03/04/opinion/exponential-language-math.html

 

[CWatters]

Ohh so you say my mistake is how I calculate square area? So an area of 2cm^2 isn't equale to a square with sides of length 2 cm?

Correct. 2cm^2 would be the area of a rectangle 2cm * 1cm.