Question

4a. Find the radius of a circle with an area of 1,809.56 square centimeters. How did you calculate it?

A = πr2


You must show ALL work for full credit.

(2 points)

Answer 1

To find the radius of a circle given its area, we can use the formula for the area of a circle:

\[ A = \pi r^2 \]

Where:
- \( A \) is the area of the circle.
- \( r \) is the radius of the circle.
- \( \pi \) (pi) is approximately 3.14159.

Given that the area \( A = 1,809.56 \) square centimeters, we can rearrange the formula to solve for the radius \( r \):

1. Start with the area formula:

\[
A = \pi r^2
\]

2. Substitute the known area into the equation:

\[
1,809.56 = \pi r^2
\]

3. To isolate \( r^2 \), divide both sides by \( \pi \):

\[
r^2 = \frac{1,809.56}{\pi}
\]

4. Now, using \( \pi \approx 3.14159 \):

\[
r^2 = \frac{1,809.56}{3.14159}
\]

5. Calculate the right side:

\[
r^2 \approx \frac{1,809.56}{3.14159} \approx 576.00
\]

6. Now, take the square root of both sides to find \( r \):

\[
r = \sqrt{576.00}
\]

7. Calculate the square root:

\[
r \approx 24.00 \text{ cm}
\]

Thus, the radius of the circle is approximately **24.00 centimeters**.

### Final Answer:
**Radius = 24.00 cm**.