How do i calculate square miles in a circle?

[2Xtreme21]

Originally posted by: spidey07
I don't think square miles or area measurements of land care about topology changes. It's a measure of distance, not the distance as you walk it.

:thumbsup:

It's defined as area as the crow flies.

 

[EagleKeeper]

Originally posted by: dullard
Note: if you are talking land area, then the answer is far greater than pi*r^2. Why? Land is hilly, and hilly land has more surface area than a hypothetical perfectly flat circle.

In an area that large, you'll get lots of peaks and valleys if we are talking about Earth.

What happens when you count caves?

 

[Mermaidman]

Originally posted by: EagleKeeper

Originally posted by: dullard
Note: if you are talking land area, then the answer is far greater than pi*r^2. Why? Land is hilly, and hilly land has more surface area than a hypothetical perfectly flat circle.

In an area that large, you'll get lots of peaks and valleys if we are talking about Earth.

What happens when you count caves?

Those would be subtracted And DON'T even mention wormholes.

 

[Paddington]

You've never heard of Pi * radius^2?

 

[tomywishbone]

"Who wants pie & punch?" -E. Cartman

 

[Pacemaker]

Wow and all this time I thought Pie was round, guess I was wrong.

Man that is a bad joke, I should be banned for that

 

[gsethi]

I hope he knows that:
radius = 0.5 x Diameter

else his next question will be on how to find radius of a circle

 

[dullard]

Originally posted by: EagleKeeper
What happens when you count caves?

I didn't even think of caves. We could go on and on. It does depend on the important piece of information. Do we want to know how much of the sun's energy reaches the ground? If so, caves are mostly meaningless. If we want to know how many bacteria there are, then the caves could support bacteria life.

I'm trying to come up with something funny or interesting to say on this topic, but I've hit a typers block.

 

[dullard]

Originally posted by: mercanucaribe
Land area is never calculated like that AFAIK and I'm a geographer. An acre is a land unit on the datum not the 3d topography.

If you use the actual area of the terrain, you'd have to arbitrarily decide what resolution DEM to use. Areas would be different depending on whether you use 10m pixels, or 1cm pixels. If the pixels were infintely small, area for any section of land would be infinite, for the same reason that a coastline length continually gets longer as you increase resolution used to measure it.

For mineral rights it wouldn't matter, and for farming it would be moot because soil on a slope is less fertile. You can't build a tilted house either.

Legally, you are correct and for many other purposes you are correct. Heck, read my later post on resolution and coastlines. But for many other puposes you are 100% incorrect. For example, if you need to know how much paint to cover a surface, then topography matters. If you need to know how much heat will be lossed/gained then topography matters. There is a reason heat sinks have fins, more surface area. Suppose you had a circular heat sink, would you say the surface area is pi*r^2? Of course not. I could go on and on.

 

[meltdown75]

Originally posted by: dullard

Originally posted by: mercanucaribe
Land area is never calculated like that AFAIK and I'm a geographer. An acre is a land unit on the datum not the 3d topography.

If you use the actual area of the terrain, you'd have to arbitrarily decide what resolution DEM to use. Areas would be different depending on whether you use 10m pixels, or 1cm pixels. If the pixels were infintely small, area for any section of land would be infinite, for the same reason that a coastline length continually gets longer as you increase resolution used to measure it.

For mineral rights it wouldn't matter, and for farming it would be moot because soil on a slope is less fertile. You can't build a tilted house either.

Legally, you are correct and for many other purposes you are correct. Heck, read my later post on resolution and coastlines. But for many other puposes you are 100% incorrect. For example, if you need to know how much paint to cover a surface, then topography matters. If you need to know how much heat will be lossed/gained then topography matters. There is a reason heat sinks have fins, more surface area. Suppose you had a circular heat sink, would you say the surface area is pi*r^2? Of course not. I could go on and on.

Dude, he's a freaking GEOGRAPHER. You = pwned.

 

[Hyperion042]

Originally posted by: mercanucaribe
If you use the actual area of the terrain, you'd have to arbitrarily decide what resolution DEM to use. Areas would be different depending on whether you use 10m pixels, or 1cm pixels. If the pixels were infintely small, area for any section of land would be infinite, for the same reason that a coastline length continually gets longer as you increase resolution used to measure it.

Somebody didn't pay attention in Calculus. Only in the case of a fractal surface would you get an infinite surface area - since atoms are ultimatley round, you would come out with a large but finite surface area, the point being that since as you get down to smaller scales the areas involved reduce with the square of the distance being measured. Such a measurement on infinitely fine points would come out with a finite surface area, but I agree that the point is nitpicky.

 

[LordNoob]

What about the fact that in addition to the hills, peaks and valleys... the fact that since the earth is a sphere, a circle of the surface of the earth will be convex?

 

[Mark R]

Originally posted by: LordNoob
What about the fact that in addition to the hills, peaks and valleys... the fact that since the earth is a sphere, a circle of the surface of the earth will be convex?

Delete me. I'm talking nonsense.

 

[LordNoob]

Ok nevermind. I thought about it more and if you took a circle measured on the surface of the earth, if you were able to account for all inclines and declines in elevation perfectly and exactly, you don't have to account for the curvature of the earth because that will already be factored in.

 

[Mark R]

Originally posted by: LordNoob
If you take a 2 dimensional circle made of rubber and stretch it out by pushing on the center until it is shaped like a bowl, it will have greater surface area. This is my point.

But in your example, you are taking a flat shape and stretching it - of course that will increase the area.

However, the rest of the explanation that used to go here, was gibberish. So, it's gone.

 

[mercanucaribe]

Originally posted by: Mark R

Originally posted by: LordNoob
What about the fact that in addition to the hills, peaks and valleys... the fact that since the earth is a sphere, a circle of the surface of the earth will be convex?

If the radius of the 'circle' is measured along the surface of the earth then it doesn't matter. The same method of calculation (pr²) can be used. This even works for the more complex oblate case.

Whoa... That's pretty awesome.
Wait.. does that mean that the surface area of a sphere is p(.5*circumference)^2?? That can't be right because by the time you get to the other pole, the area increases a smaller amount for every increase in latitude.. With a 2d circle, area would be increasing a greater amount because the circle is bigger at that point.

 

[DrPizza]

Originally posted by: dullard

Originally posted by: mercanucaribe
Land area is never calculated like that AFAIK and I'm a geographer. An acre is a land unit on the datum not the 3d topography.

If you use the actual area of the terrain, you'd have to arbitrarily decide what resolution DEM to use. Areas would be different depending on whether you use 10m pixels, or 1cm pixels. If the pixels were infintely small, area for any section of land would be infinite, for the same reason that a coastline length continually gets longer as you increase resolution used to measure it.

For mineral rights it wouldn't matter, and for farming it would be moot because soil on a slope is less fertile. You can't build a tilted house either.

Legally, you are correct and for many other purposes you are correct. Heck, read my later post on resolution and coastlines. But for many other puposes you are 100% incorrect. For example, if you need to know how much paint to cover a surface, then topography matters. If you need to know how much heat will be lossed/gained then topography matters. There is a reason heat sinks have fins, more surface area. Suppose you had a circular heat sink, would you say the surface area is pi*r^2? Of course not. I could go on and on.

" and for many other purposes you are correct."
Include the purpose of figuring out how many square miles there are in a 340 mile diameter circle.

 

[spacejamz]

should the phrase "anal-retentive" have a hyphen or not?

 

[Amused]

I like pi

 

[theprodigalrebel]

Hey, any one know the keystroke for 'pi' in Windows? I can't seem to find it in Character Map.

 

[Tom]

suppose the question was how many actual square miles would fit ?

as in full square miles that are square, with sides one mile long.

 

[Mark R]

Originally posted by: theprodigalrebel
Hey, any one know the keystroke for 'pi' in Windows? I can't seem to find it in Character Map.

You can either copy & paste from 'Character map'.

Alternatively you can type it as ALt + (Numpad +) 3C0.

N.B. This shortcut only works if you've got EnableHexNumpad enabled in the registry (google will tell you how to sort this out).

If you don't want to edit the registry, and the mode above doesn't work, then you can try Alt + (Numpad 960) - but this only works in Word/Wordpad/etc. not in Firefox/mozilla/other apps.

 

[JSFLY]

Originally posted by: CycloWizard

Originally posted by: pnad
Correct 90792.03 Square Miles
pi*r^2

Wrong. 91,000 square miles. Sig figs.

Sig figs or significant digits?

 

[Mark R]

Originally posted by: mercanucaribe
Whoa... That's pretty awesome.
Wait.. does that mean that the surface area of a sphere is p(.5*circumference)^2?? That can't be right because by the time you get to the other pole, the area increases a smaller amount for every increase in latitude.. With a 2d circle, area would be increasing a greater amount because the circle is bigger at that point.

Good spot.

The correct formula for a spherical surface is as follows:
r = radius of circle on the surface.
R = radius of sphere

A = 2 p R² [1 - cos (r / R)]

This time, I've checked it and it does work. Although, if the circle radius is small compared to the radius of the sphere the results are very close.

So, going back to the original problem of a circle with 340 mile diameter:

R = 3963.2 miles
r = 170 miles

A = 90800 square miles.