Question

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

Answer 1

To find the area of a circle when the circumference is given, we can use the relationship between the circumference and the radius.

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

\[
C = 2\pi r
\]

Given that the circumference is \( 22\pi \):

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

We can simplify this by dividing both sides by \( 2\pi \):

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

Now that we have the radius, we can find the area \( A \) of the circle using the formula for area:

\[
A = \pi r^2
\]

Substituting \( r = 11 \) inches:

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

Now using \( \pi \approx 3.14 \):

\[
A \approx 121 \times 3.14
\]

Calculating this:

\[
A \approx 379.94
\]

Thus, the area of the circle, expressed to the hundredths place, is:

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