The exact circumference of a circle is \( 18 \pi \) inches. What is the approximate area of th circle? Use 3.14 for \( \pi \). Round to the neares hundredth if necessary. (Example 4 )

To find the approximate area of the circle given its circumference, follow these steps: 1. **Given:** - Circumference (\( C \)) = \( 18\pi \) inches - Use \( \pi \approx 3.14 \) 2. **Find the Radius (\( r \)):** The formula for the circumference of a circle is: \[ C = 2\pi r \] Plugging in the given circumference: \[ 18\pi = 2\pi r \] Divide both sides by \( 2\pi \): \[ r = \frac{18\pi}{2\pi} = 9 \text{ inches} \] 3. **Calculate the Area (\( A \)):** The formula for the area of a circle is: \[ A = \pi r^2 \] Plugging in the radius: \[ A = \pi \times 9^2 = \pi \times 81 \] Using \( \pi \approx 3.14 \): \[ A \approx 3.14 \times 81 = 254.34 \text{ square inches} \] **Answer:** The approximate area of the circle is 254.34 square inches.