SOLUTION: If the radius of a circle is 3 and is located inside of a square touching all 4 sides, what is the area of the 4 corners of the square? (Use 3.14 for pi) This is multiple choice

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Question 74860: If the radius of a circle is 3 and is located inside of a square touching all 4 sides, what is the area of the 4 corners of the square? (Use 3.14 for pi)
This is multiple choice question. Need to see the formula that is used.
Multiple choice answers:
A. 5.15 sq units
B. 17.16 sq units
C. 7.74 sq units
D. 21.72 sq units
Thank you!
Found 2 solutions by jim_thompson5910, psbhowmick:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you drew a picture, you would see that the sides of the square equal the diameter (2r) of the circle. So the area of the circle is:
A=pi%2Ar%5E2
A=pi%2A3%5E2
A=9pi
The area of the square is:
A=L%2Aw
A=2r%2A2r
A=4r%5E2
A=4%283%29%5E2
A=36
So the area of the corners of the square is the difference of the circle and the square.
Area_of_corners=%28Area_of_square%29-%28Area_of_circle%29
Area_of_corners=%2836%29-%289pi%29
Area_of_corners=36-9%283.14%29Since we're using 3.14 for pi then plug in 3.14
Area_of_corners=36-28.26
Area_of_corners=7.74
So the area of the corners is 7.74 sq units which means the answer is c)

Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
(c) is correct

Area of the circle = pi%2Ar%5E2+=+3.14%2A3%5E2+=+3.14%2A9+=+31.4+-+3.14+=+28.26 sq. units.

The side of the square is a+=+2r+=+6.
Area of the square = a%5E2+=+6%5E2+=+36 sq. units

Reqd. area = (Area of the square) - (Area of the circle) = 36 - 28.26 = 7.74 sq. units.