The area of a circle if \(154\)cm\(^2\). Find its circumference. (Take \(\pi = \frac{22}{7}\))
Explanation
To find the circumference of a circle when the area is given, follow these steps:
1. Calculate the radius:
Given:
\[
\text{Area} = 154 \text{ cm}^2
\]
Use the formula for the area of a circle:
\[
\text{Area} = \pi r^2
\]
Substitute \(\pi = \frac{22}{7}\):
\[
154 = \frac{22}{7} r^2
\]
Solve for \(r^2\):
\[
r^2 = \frac{154 \times 7}{22} = 49
\]
Find \(r\):
\[
r = \sqrt{49} = 7 \text{ cm}
\]
2. Calculate the circumference:
Use the formula for the circumference:
\[
\text{Circumference} = 2 \pi r
\]
Substitute \(r = 7 \text{ cm}\) and \(\pi = \frac{22}{7}\):
\[
\text{Circumference} = 2 \times \frac{22}{7} \times 7 = 44 \text{ cm}
\]
The correct answer is: D. 44 cm