To determine the radius of a circle given its area, we use the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Where:
- [tex]\( A \)[/tex] is the area of the circle,
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14159).
Given the area [tex]\( A = 25 \pi \)[/tex] square meters, we need to find the radius [tex]\( r \)[/tex].
1. Write down the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
2. Substitute the given area into the formula:
[tex]\[ 25 \pi = \pi r^2 \][/tex]
3. Divide both sides of the equation by [tex]\(\pi\)[/tex] to isolate [tex]\(r^2\)[/tex]:
[tex]\[ \frac{25 \pi}{\pi} = r^2 \][/tex]
[tex]\[ 25 = r^2 \][/tex]
4. Solve for [tex]\(r\)[/tex] by taking the square root of both sides:
[tex]\[ r = \sqrt{25} \][/tex]
5. Calculate the square root of 25:
[tex]\[ r = 5 \][/tex]
Thus, the radius of the circle is:
[tex]\[ r = 5 \text{ meters} \][/tex]
