Question

The area of a circle is 154 cm². What is the circumference of the circle? (Use π = 22/7)

• A. \(22 \text{ cm} \)
• B. \(44 \text{ cm} \)
• C. \(66 \text{ cm} \)
• D. \(88 \text{ cm} \)

Hint:

In competitive exams, circles with standard measurements appear very frequently. Memorizing this foundational radius pair will save you valuable calculation time: - If Radius \((r) = 7\text{ cm} \implies \text{Area} = 154\text{ cm}^2\) and \(\text{Circumference} = 44\text{ cm}\). Recognizing the area \(154\text{ cm}^2\) instantly tells you that \(r = 7\), allowing you to determine the circumference as \(44\text{ cm}\) within a few seconds without doing any scratch work!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The area of a circle measures the two-dimensional space enclosed within its perimeter, whereas the circumference represents the total linear distance around the outside boundary. Both properties depend entirely on the radius of the circle. To find the circumference when given only the area, we must first solve for the unknown radius and then substitute that radius into the circumference formula.

Step 2: Key Formula or Approach:
1. \(\text{Area of a Circle } (A) = \pi r^2\)
2. \(\text{Circumference of a Circle } (C) = 2\pi r\)
where \(r\) is the radius of the circle and \(\pi = \frac{22}{7}\).

Step 3: Detailed Explanation:
Given that the total area of the circle is \(154\text{ cm}^2\): \[ \pi r^2 = 154 \] Substitute the given value of \(\pi = \frac{22}{7}\) into the equation: \[ \frac{22}{7} \times r^2 = 154 \] Isolate the \(r^2\) term by multiplying both sides by the reciprocal fraction \(\frac{7}{22}\): \[ r^2 = 154 \times \frac{7}{22} \] \[ r^2 = 7 \times 7 \] \[ r^2 = 49 \] Take the square root of both sides to find the radius \(r\): \[ r = \sqrt{49} = 7\text{ cm} \] Now, substitute the calculated radius \(r = 7\text{ cm}\) into the circumference formula: \[ C = 2 \times \frac{22}{7} \times 7 \] \[ C = 2 \times 22 = 44\text{ cm} \]

Step 4: Final Answer:
The circumference of the circle is 44 cm.