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Answer :
The area of the circle is [tex]\(121\pi\)[/tex] square inches.
Let's solve it step by step:
1. Given: The circumference of the circle is [tex]\( 22\pi \)[/tex] inches.
2. Formula for Circumference: The circumference of a circle is given by the formula [tex]\( C = 2\pi r \),[/tex] where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius of the circle.
3. Finding the Radius: We can rearrange the formula to solve for [tex]\( r \)[/tex]:
[tex]\[ C = 2\pi r \][/tex]
[tex]\[ 22\pi = 2\pi r \][/tex]
Dividing both sides by [tex]\( 2\pi \)[/tex], we get:
[tex]\[ r = \frac{22\pi}{2\pi} \][/tex]
[tex]\[ r = 11 \][/tex]
4. Finding the Area: The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex].
Plugging in the value of [tex]\( r \)[/tex] we found (which is 11), we get:
[tex]\[ A = \pi (11)^2 \][/tex]
[tex]\[ A = 121\pi \][/tex]
5. Final Answer: The area of the circle is [tex]\( 121\pi\)[/tex] square inches.
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Rewritten by : Barada
Answer:
A = 121 pi in^2
Step-by-step explanation:
The circumference is given by
C = 2 * pi*r
22 pi = 2 * pi *r
Divide each side by 2 pi
22 pi / (2 pi) = 2 pi r / (2pi)
11 = r
Now find the area
A = pi r^2
A = pi (11)^2
A = 121 pi in^2
