Question

4a. Find the radius of a circle with an area of 1809.56 square centimeters. How did you calculate it?
A = πr^2
A = πr^2A = 1809.56 1809.56 = 3.14r^2 divide each side y 3.14r^2 = 1809.56/ 3.14 = 576r=square root of 576 = 24
4b. What is the circumference for the same circle? How did you calculate it?
C = 2πr

Answer 1

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

\[ A = \pi r^2 \]

4a. **Finding the radius:**

Given the area \( A = 1809.56 \) square centimeters, we can rearrange the formula to solve for \( r \):

\[
r^2 = \frac{A}{\pi}
\]

Using \( \pi \approx 3.14 \):

\[
r^2 = \frac{1809.56}{3.14} \approx 576
\]

Next, take the square root of both sides to find \( r \):

\[
r = \sqrt{576} = 24 \text{ cm}
\]

So, the radius of the circle is **24 centimeters**.

---

4b. **Finding the circumference:**

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

\[
C = 2\pi r
\]

Using the radius we calculated:

\[
C = 2 \times 3.14 \times 24
\]

Calculating this gives:

\[
C = 6.28 \times 24 \approx 150.72 \text{ cm}
\]

Therefore, the circumference of the circle is approximately **150.72 centimeters**.