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Answer :
Certainly! Let's solve this problem step by step.
1. Understand What is Given:
You are given the circumference of a circle, which is [tex]\(22\pi\)[/tex] inches.
2. Recall the Formula for Circumference:
The formula for the circumference [tex]\(C\)[/tex] of a circle is [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle.
3. Set Up the Equation:
Since the circumference is [tex]\(22\pi\)[/tex], we have:
[tex]\[
2\pi r = 22\pi
\][/tex]
4. Solve for the Radius [tex]\(r\)[/tex]:
To find the radius, divide both sides of the equation by [tex]\(2\pi\)[/tex]:
[tex]\[
r = \frac{22\pi}{2\pi}
\][/tex]
When you simplify the equation, you get:
[tex]\[
r = \frac{22}{2} = 11
\][/tex]
So, the radius of the circle is 11 inches.
5. Recall the Formula for Area:
The area [tex]\(A\)[/tex] of a circle is given by the formula [tex]\(A = \pi r^2\)[/tex].
6. Calculate the Area:
Substitute the radius (11 inches) into the area formula:
[tex]\[
A = \pi \times (11)^2
\][/tex]
[tex]\[
A = \pi \times 121
\][/tex]
[tex]\[
A = 121\pi
\][/tex]
Therefore, the area of the circle, in square inches, expressed in terms of [tex]\(\pi\)[/tex], is [tex]\(121\pi\)[/tex] square inches.
1. Understand What is Given:
You are given the circumference of a circle, which is [tex]\(22\pi\)[/tex] inches.
2. Recall the Formula for Circumference:
The formula for the circumference [tex]\(C\)[/tex] of a circle is [tex]\(C = 2\pi r\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle.
3. Set Up the Equation:
Since the circumference is [tex]\(22\pi\)[/tex], we have:
[tex]\[
2\pi r = 22\pi
\][/tex]
4. Solve for the Radius [tex]\(r\)[/tex]:
To find the radius, divide both sides of the equation by [tex]\(2\pi\)[/tex]:
[tex]\[
r = \frac{22\pi}{2\pi}
\][/tex]
When you simplify the equation, you get:
[tex]\[
r = \frac{22}{2} = 11
\][/tex]
So, the radius of the circle is 11 inches.
5. Recall the Formula for Area:
The area [tex]\(A\)[/tex] of a circle is given by the formula [tex]\(A = \pi r^2\)[/tex].
6. Calculate the Area:
Substitute the radius (11 inches) into the area formula:
[tex]\[
A = \pi \times (11)^2
\][/tex]
[tex]\[
A = \pi \times 121
\][/tex]
[tex]\[
A = 121\pi
\][/tex]
Therefore, the area of the circle, in square inches, expressed in terms of [tex]\(\pi\)[/tex], is [tex]\(121\pi\)[/tex] square inches.
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