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)4b. What is the circumference for the same circle? How did you calculate it?

C = 2πr

You must show ALL work for full credit.

(2 points)

Answer 1

To solve for the radius and circumference of a circle given its area, we will use the formulas you provided.

### Part 4a: Finding the Radius

The formula for the area \( A \) of a circle is given by:

\[
A = \pi r^2
\]

We are given that the area \( A \) is 1,809.56 square centimeters, so we can set up the equation:

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

To solve for \( r^2 \), we first divide both sides by \( \pi \):

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

Using the approximate value of \( \pi \) (3.14159), we substitute it into the equation:

\[
r^2 = \frac{1,809.56}{3.14159} \approx 575.00
\]

Next, we find \( r \) by taking the square root of both sides:

\[
r = \sqrt{575.00} \approx 24.08 \text{ cm}
\]

Thus, the radius of the circle is approximately **24.08 cm**.

---

### Part 4b: Finding the Circumference

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

\[
C = 2\pi r
\]

Now that we have found the radius \( r \approx 24.08 \text{ cm} \), we can substitute this value into the circumference formula:

\[
C = 2\pi(24.08)
\]

Calculating this gives:

\[
C \approx 2 \times 3.14159 \times 24.08 \approx 150.81 \text{ cm}
\]

Thus, the circumference of the circle is approximately **150.81 cm**.

### Summary of Results:
- **Radius:** \( \approx 24.08 \text{ cm} \)
- **Circumference:** \( \approx 150.81 \text{ cm} \)