Answer :
To solve the problem of finding the area of a circle when its circumference is given as 22 inches, we can follow these steps:
1. Understand the Relationship:
- The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Find the Radius:
- We need to find the radius [tex]\( r \)[/tex] using the circumference:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
- Substitute the given circumference:
[tex]\[
r = \frac{22}{2 \pi} \approx 3.5
\][/tex]
3. Calculate the Area:
- The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
- Substitute the value of [tex]\( r \)[/tex] we found:
[tex]\[
A = \pi (3.5)^2
\][/tex]
- This calculation gives an area of approximately 38.52 square inches.
Thus, the area of the circle, in square inches, is approximately [tex]\(38.52\)[/tex].
1. Understand the Relationship:
- The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
2. Find the Radius:
- We need to find the radius [tex]\( r \)[/tex] using the circumference:
[tex]\[
r = \frac{C}{2 \pi}
\][/tex]
- Substitute the given circumference:
[tex]\[
r = \frac{22}{2 \pi} \approx 3.5
\][/tex]
3. Calculate the Area:
- The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
- Substitute the value of [tex]\( r \)[/tex] we found:
[tex]\[
A = \pi (3.5)^2
\][/tex]
- This calculation gives an area of approximately 38.52 square inches.
Thus, the area of the circle, in square inches, is approximately [tex]\(38.52\)[/tex].
