Question

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

• A. 36 cm
• B. 22 cm
• C. 48 cm
• D. 44 cm

Hint:

Since the options give circumference values, try converting each option back into a radius and check which one reproduces the given area of 154 cm squared.

Answer 1

The Correct Option is D

Step 1: Instead of solving algebraically for the radius first, test the given options by working backward from each candidate circumference.
Step 2: For any circle, if the circumference is $C$, then radius $r=\frac{C}{2\pi}$, and the area is $\pi r^2 = \pi\left(\frac{C}{2\pi}\right)^2=\frac{C^2}{4\pi}$. This lets us check each option against the given area of $154$ cm$^2$ directly.
Step 3: Try option "44 cm": $r=\frac{44}{2\times\frac{22}{7}}=\frac{44\times7}{44}=7$ cm.
Step 4: Compute the area for this radius: Area $=\pi r^2=\frac{22}{7}\times7\times7=22\times7=154$ cm$^2$.
Step 5: This matches the given area of $154$ cm$^2$ exactly, so the circumference must be $44$ cm. (Any other option would give a radius that does not reproduce the area 154 cm$^2$.) \[\boxed{44\ \text{cm}}\]