Question

Henry knows that the circumference of a circle is 18Pi inches. What is the area of the circle?
36 pi inches squared
81 pi inches squared
162 pi inches squared
324 pi inches squared

Answer 1

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

The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius.

Given that the circumference is \( 18\pi \) inches, we can set up the equation:
\[
2\pi r = 18\pi
\]

Now, we can divide both sides by \( 2\pi \):
\[
r = \frac{18\pi}{2\pi} = \frac{18}{2} = 9 \text{ inches}
\]

Now that we have the radius, we can calculate the area \( A \) of the circle using the formula:
\[
A = \pi r^2
\]

Substituting the radius we found:
\[
A = \pi (9)^2 = \pi \cdot 81 = 81\pi \text{ inches squared}
\]

Therefore, the area of the circle is \( \boxed{81\pi} \) inches squared.