To determine the radius of a circle, given its area and using the provided value of [tex]\(\pi = \frac{22}{7}\)[/tex], we can follow these detailed steps:
1. Understanding the formula:
The area [tex]\(A\)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\(r\)[/tex] is the radius.
2. Rearranging the formula:
To find the radius [tex]\(r\)[/tex], we need to rearrange the formula:
[tex]\[
r^2 = \frac{A}{\pi}
\][/tex]
[tex]\[
r = \sqrt{\frac{A}{\pi}}
\][/tex]
3. Substitute given values:
We are given:
[tex]\[
A = 2464 \, \text{m}^2
\][/tex]
[tex]\(\pi = \frac{22}{7}\)[/tex]
4. Calculate the radius:
First, calculate [tex]\(\frac{A}{\pi}\)[/tex]:
[tex]\[
\frac{2464}{\frac{22}{7}} = 2464 \times \frac{7}{22}
\][/tex]
Simplifying inside the fraction:
[tex]\[
\frac{2464 \times 7}{22} = \frac{17248}{22} = 784
\][/tex]
Now, take the square root of 784:
[tex]\[
r = \sqrt{784} = 28 \, \text{meters}
\][/tex]
5. Convert radius to centimeters:
Since 1 meter = 100 centimeters, we convert the radius from meters to centimeters:
[tex]\[
28 \, \text{m} = 28 \times 100 \, \text{cm} = 2800 \, \text{cm}
\][/tex]
6. Identify the correct option:
The options given are:
(a) 24 cm
(b) 26 cm
(c) 28 cm
(d) 56 cm
The correct radius in centimeters is:
(c) 28 cm
Hence, given the area of the circle as [tex]\(2464 \, \text{m}^2\)[/tex], the radius of the circle in centimeters is [tex]\( \boxed{28} \)[/tex].
