The circumference of a circle is 22π

inches. Find the area of that circle. Substitute 3.14
for pi. Express your answer to the hundredths place.(1 point)
in.2

1 answer

To find the area of the circle, we first need to determine its radius using the given circumference.

The formula for the circumference \( C \) of a circle is:

\[ C = 2\pi r \]

Given that the circumference is \( 22\pi \) inches, we can set up the equation:

\[ 2\pi r = 22\pi \]

To isolate \( r \), we can divide both sides by \( 2\pi \):

\[ r = \frac{22\pi}{2\pi} = 11 \text{ inches} \]

Now we can use the radius to find the area \( A \) of the circle. The formula for the area is:

\[ A = \pi r^2 \]

Substituting \( r = 11 \) inches into the area formula:

\[ A = \pi \times (11)^2 = \pi \times 121 \]

Next, we substitute \( 3.14 \) for \( \pi \):

\[ A = 3.14 \times 121 \]

Calculating this:

\[ A = 3.14 \times 121 = 379.94 \]

Thus, the area of the circle is:

\[ \boxed{379.94} \text{ in}^2 \]