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Answer :
To find the area of a circle when the circumference is given, follow these steps:
1. Understand the relationship between circumference and radius:
The formula for the circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[
C = 2\pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Use the given circumference:
We are given that the circumference is [tex]\( 22\pi \)[/tex] inches. Set the formula equal to the given value:
[tex]\[
2\pi r = 22\pi
\][/tex]
3. Solve for the radius [tex]\( r \)[/tex]:
To find the radius, divide both sides of the equation by [tex]\( 2\pi \)[/tex]:
[tex]\[
r = \frac{22\pi}{2\pi} = 11
\][/tex]
So, the radius of the circle is 11 inches.
4. Use the radius to find the area of the circle:
The formula for the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
Substitute the radius [tex]\( r = 11 \)[/tex] into the formula:
[tex]\[
A = \pi \times (11)^2 = \pi \times 121
\][/tex]
5. Express the area in terms of [tex]\( \pi \)[/tex]:
Therefore, the area of the circle is:
[tex]\[
121\pi
\][/tex]
square inches.
That's the step-by-step process to find the area when the circumference is given. The correct result is that the area of the circle is [tex]\( 121\pi \)[/tex] square inches.
1. Understand the relationship between circumference and radius:
The formula for the circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[
C = 2\pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Use the given circumference:
We are given that the circumference is [tex]\( 22\pi \)[/tex] inches. Set the formula equal to the given value:
[tex]\[
2\pi r = 22\pi
\][/tex]
3. Solve for the radius [tex]\( r \)[/tex]:
To find the radius, divide both sides of the equation by [tex]\( 2\pi \)[/tex]:
[tex]\[
r = \frac{22\pi}{2\pi} = 11
\][/tex]
So, the radius of the circle is 11 inches.
4. Use the radius to find the area of the circle:
The formula for the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
Substitute the radius [tex]\( r = 11 \)[/tex] into the formula:
[tex]\[
A = \pi \times (11)^2 = \pi \times 121
\][/tex]
5. Express the area in terms of [tex]\( \pi \)[/tex]:
Therefore, the area of the circle is:
[tex]\[
121\pi
\][/tex]
square inches.
That's the step-by-step process to find the area when the circumference is given. The correct result is that the area of the circle is [tex]\( 121\pi \)[/tex] square inches.
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