Question

. 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.

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,
- \( r \) is the radius, and
- \( \pi \) is a constant approximately equal to 3.14159.

Given 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 value of \( A \):
\[
1,809.56 = \pi r^2
\]

3. Divide both sides by \( \pi \):
\[
r^2 = \frac{1,809.56}{\pi}
\]

4. Now, use \( \pi \approx 3.14159 \):
\[
r^2 = \frac{1,809.56}{3.14159}
\]

5. Calculate the right side:
\[
r^2 \approx \frac{1,809.56}{3.14159} \approx 575.38
\]

6. Finally, take the square root of both sides to find \( r \):
\[
r = \sqrt{575.38} \approx 24.0 \text{ cm}
\]

So, the radius of the circle is approximately **24.0 centimeters**.