SOLUTION: Question Find the difference between the perimeter of a square of area 1 m^2 (metre square) and the circumference of a circle of the same area. Plese help to answer. Thank y

Algebra ->  Surface-area -> SOLUTION: Question Find the difference between the perimeter of a square of area 1 m^2 (metre square) and the circumference of a circle of the same area. Plese help to answer. Thank y      Log On


   

Question 42074: Question
Find the difference between the perimeter of a square of area 1 m^2 (metre square) and the circumference of a circle of the same area.
Plese help to answer. Thank you.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
1 metre square means a square with side 1 m. Don't confuse it with square metre.

Its area = 1 x 1 = 1 sq m.
Perimeter = 4 x (Length of side) = 4 x 1 = 4 m.

Let the radius of the circle be 'r' metre.
Then its area = pi%2Ar%5E2.
The area of this circle is equal to that of the square.
So, pi%2Ar%5E2+=+1
or r%5E2+=+1%2F%28pi%29
or r+=+sqrt%281%2F%28pi%29%29
or r = 0.5642 m.

Hence, circumference of the circle = 2%2A%28pi%29%2Ar = 2%2A%28pi%29%2A0.5642 = 3.545 m.

So the difference between the perimeter of the square and circumference of the circle = 4 - 3.545 = 0.455 m