Certainly! Let's solve the problem step-by-step:
1. Understand the relationship between the area and the radius of a circle:
The area [tex]\( A \)[/tex] of a circle is related to its radius [tex]\( r \)[/tex] by the formula:
[tex]\[
A = \pi r^2
\][/tex]
Here, [tex]\( A \)[/tex] represents the area and [tex]\( r \)[/tex] represents the radius.
2. Given Data:
The area of the pond, [tex]\( A \)[/tex], is given as [tex]\( 314 \, \text{m}^2 \)[/tex].
3. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[
r^2 = \frac{A}{\pi}
\][/tex]
Consequently:
[tex]\[
r = \sqrt{\frac{A}{\pi}}
\][/tex]
4. Substitute the given area into the formula:
Here, [tex]\( A = 314 \, \text{m}^2 \)[/tex].
5. Finally, calculate the radius [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{\frac{314}{\pi}}
\][/tex]
Using the value [tex]\( \pi \approx 3.14159 \)[/tex], we get:
[tex]\[
r \approx 9.997 \, \text{meters}
\][/tex]
Thus, the radius of the circular pond is approximately [tex]\( 9.997 \, \text{meters} \)[/tex].
