To find the radius of a circle given its area, we need to use the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where [tex]\( A \)[/tex] is the area and [tex]\( r \)[/tex] is the radius. Given that the area ([tex]\( A \)[/tex]) is 11.5 square centimeters, we can solve for [tex]\( r \)[/tex] as follows:
1. Start with the equation:
[tex]\[
A = \pi r^2
\][/tex]
2. Substitute the given area into the equation:
[tex]\[
11.5 = \pi r^2
\][/tex]
3. To isolate [tex]\( r^2 \)[/tex], divide both sides by [tex]\(\pi\)[/tex]:
[tex]\[
r^2 = \frac{11.5}{\pi}
\][/tex]
4. Now, take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{\frac{11.5}{\pi}}
\][/tex]
5. Calculate the numerical value:
[tex]\[
r = \sqrt{\frac{11.5}{3.14159}} \approx \sqrt{3.66} \approx 1.91
\][/tex]
Thus, after approximating the square root, we find the radius of the circle to be about 1.91 cm.
This matches option a:
[tex]\[ a\) \text{ about 1.91 cm} \][/tex]
So, the correct answer is [tex]\( a \)[/tex].
