Question

The area of a circle is \(154 \text{ }cm^2\). Find the circumference of the circle. Take \(\pi=\frac{22}{7}\)

• A. 22 cm
• B. 28 cm
• C. 44 cm
• D. 56 cm

Answer 1

The Correct Option is C

We are given the area of a circle as \(154 \text{ cm}^2\) and need to find its circumference. The formula for the area of a circle is:

\(A = \pi r^2\)

Given \(A = 154 \text{ cm}^2\) and \(\pi = \frac{22}{7}\), we have:

\(154 = \frac{22}{7} r^2\)

To solve for \(r^2\), multiply both sides by \(\frac{7}{22}\):

\(r^2 = 154 \times \frac{7}{22}\)

Calculate the result:

\(r^2 = 49\)

Now, solve for \(r\):

\(r = \sqrt{49} = 7\text{ cm}\)

Next, find the circumference of the circle using the formula:

\(C = 2\pi r\)

Substitute the values: \(r = 7\) and \(\pi = \frac{22}{7}\):

\(C = 2 \times \frac{22}{7} \times 7\)

Simplify the expression:

\(C = 44\text{ cm}\)

Therefore, the circumference of the circle is 44 cm.