SOLUTION: Find the perimeter of the square in which a circle of area 81 pi is inscribed. A. 81 B. 40 C. 72 D. 9 E. 18 Please show me step by step how to solve the answer. Thank you

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Question 281602: Find the perimeter of the square in which a circle of area 81 pi is inscribed.
A. 81
B. 40
C. 72
D. 9
E. 18
Please show me step by step how to solve the answer.
Thank you
Found 3 solutions by Alan3354, Mathematicians, richwmiller:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Find the perimeter of the square in which a circle of area 81 pie is inscribed.
A. 81
B. 40
C. 72
D. 9
E. 18
------------
Find the radius of the circle:
Area = pi*r^2 = 81pi
r^2 = 81
r = 9
------
The square has sides 2x that, = 18
Perimeter = 4*18 = 72
Answer by Mathematicians(84)   (Show Source): You can put this solution on YOUR website!
This problem looks fun!!!
You will have to visualize a square with a circle in it, the circle has 4 points, in which it touches the middle of every square.
The Area of a circle is:

we know that
so we get:

dividing on both sides
or Since r is distance, we will only consider the positive value of r.
However, in the picture you visualized, you will see that the diameter of the circle is the length of one side of the square. A few more formulas!
Perimeter of a square: where P is perimeter and S is the length of a side.
Diameter of a circle: where r is radius and D is diameter
We get
and finally


I hope this helps ;),
Bran
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
square p=4s
circle a=pi*r^2
81*pi=pi*r^2
81=r^2
9=r
the diameter of the circle happens to be the length s
d=2r=s
2*9=18=s
4s=4*2*9
4s=72
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