SOLUTION: I need help solving the following problems: 1. A circle fits exactly inside the boundry of a square. If the square is 8cm on a side, what is the area of the shaded region insid

Algebra ->  Circles -> SOLUTION: I need help solving the following problems: 1. A circle fits exactly inside the boundry of a square. If the square is 8cm on a side, what is the area of the shaded region insid      Log On


   

Question 48252: I need help solving the following problems:
1. A circle fits exactly inside the boundry of a square. If the square is 8cm on a side, what is the area of the shaded region inside the square? Express your answer as an exact value. Put the unit cm squared after the answer.
I need to know how to set up the problem to solve it, I can't figure it out.
2. Find the area of a circle, as an approximation to the nearest square foot, fi the diameter is 2ft. Enter the unit ft squared after your answer. When rounding, round up if the next decimal is five or greater.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1) If the circle fits exactly inside the square then the diameter of the circle is exactly equal the length of the side of the square (i.e. 8 cm)
Without a diagram, I'm assuming that the "shaded area" is the area outside the circle but inside the square.
This area is the difference in the area of the square and the area of the circle, or A(s) - A(c).
The area of the square is A%28s%29+=+8%5E2 = 64 sq.cm.
The area of the circle is %28pi%29r%5E2 = %28pi%294%5E2+=+16%28pi%29sq.cm.
A%28s%29+-+A%28c%29+=+64+-+16%28pi%29 = 16%284-pi%29sq.cm. This is the area of the shaded part.
2) Find the area of a circle whose diameter is 2 ft.
The area of a circle is: %28pi%29r%5E2 where r is the radius. The radius is half the diameter, so: r+=+2%2F2 = 1 ft.
Using 3.14 as an approximation for pi, the area of this circle is:
A+=+%283.14%29%281%5E2%29 = 3.14 sq.ft. Rounded to the nearest square foot, A = 3 sq.ft.