SOLUTION: A circle is inside a square, with the diameter of circle equal to side of square. .7854 is used to determine area of circle. How is the .7854 calculated? Non-homework.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A circle is inside a square, with the diameter of circle equal to side of square. .7854 is used to determine area of circle. How is the .7854 calculated? Non-homework.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1119330: A circle is inside a square, with the diameter of circle equal to side of square. .7854 is used to determine area of circle. How is the .7854 calculated? Non-homework.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
A_square = s%5E2
A_circle = pi%2Ar%5E2+=+pi%2A%28s%2F2%29%5E2+=+pi%2As%5E2%2F4+
pi%2F4+ is 0.7854 to 4 decimal places
So A_circle = A_ square*0.7854
===================================
Dear Student:
pi+ is divided by 4 when one tries to express the area of the circle in terms of the area of the square:
A_circle = +pi%2Ar%5E2+ —> = +pi%2A%28s%2F2%29%5E2+ <<< this is A_circle in terms of the sides of the square (s). You must divide the side of the square by 2 to get the radius of the circle. After squaring, it becomes 4 in the denominator.

Continuing… = +pi%2A%28s%5E2%2F4%29+=+%28pi%2F4%29%2As%5E2+ = approx 0.7854*s%5E2 = 0.7854*A_square.

I hope you see it now.
Note that you must somehow know the area of the square (or equivalently, the side length of the square so you can calculate the area) in order to use this formula to find the area of the circle, it simply relates the two areas.