Grigori S. | Certified Physics and Math Teacher G.S.Certified Physics and Math Teacher G.S.

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The last question is incorrect. Square mile is a unit of area (two dimensional), while one mile is a unit of distnace or length (one dimensional). If you need to calculate the observable area (which is a circle, because you observe 12 miles in all directions) then just apply the standard geometric formula

A =π r^{2 }= π 12^{2} = 3.14 x 144 miles^{2} = 452.16 mi^{2}

Vladimir B. | Identify Hidden Active Causes. Imagine then Verify.Identify Hidden Active Causes. Imagine t...

4.04.0(1 lesson ratings)(1)

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Hi Teren.

The square of any measurement unit for length (square meter, square foot etc.) will be used to measure
surfaces of areas. Just by looking in one direction you will not cover a
surface.

To do that U have to look all around your current position. This way your sight will cover the area comprised between your
fixed position and the most distant still clearly visible terrain located 12 miles all around -- thus outlining a out-most still visible circle.

So what shape is the surface inside a circle -- a disk.

And which formula gives a disc's area -- π×(radius)^{2} = 3.1416 × 12^{2} = 3.1416 × 144 etc.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...

4.64.6(13 lesson ratings)(13)

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If a person can see for a distance of 12 miles, he/she can see the same distance in any direction. Therefore, he can see pi 12^2 = 144 pi square miles.