Question

The circumference of a circle is 9π cm. What is the area, in square centimeters? Express your answer in terms of piπ.

Answer 1

To find the area of a circle when given its circumference, we can start with the given circumference formula:

\[
C = 2\pi r
\]

where \( C \) is the circumference and \( r \) is the radius. We are given that the circumference is \( 9\pi \) cm:

\[
2\pi r = 9\pi
\]

To solve for the radius \( r \), we can divide both sides by \( 2\pi \):

\[
r = \frac{9\pi}{2\pi} = \frac{9}{2} \text{ cm}
\]

Next, we will use the radius to find the area \( A \) of the circle using the formula:

\[
A = \pi r^2
\]

Substituting the radius we found into the area formula, we have:

\[
A = \pi \left(\frac{9}{2}\right)^2
\]

Calculating \( \left(\frac{9}{2}\right)^2 \):

\[
\left(\frac{9}{2}\right)^2 = \frac{81}{4}
\]

Now, substituting this back into the area formula:

\[
A = \pi \cdot \frac{81}{4} = \frac{81\pi}{4}
\]

Thus, the area of the circle is

\[
\frac{81\pi}{4} \text{ square centimeters}.
\]

Therefore, the area in terms of \( \pi \) is

\[
\boxed{\frac{81\pi}{4}}.
\]