Question

The area of the circle whose circumference is equal to the perimeter of a square of side 11 cm is:

• A. 134 cm\(^2\)
• B. 124 cm\(^2\)
• C. 144 cm\(^2\)
• D. 154 cm\(^2\)

Hint:

The area of a circle can be found from the radius using the formula \( A = \pi r^2 \), and the radius can be derived from the given circumference \( C = 2 \pi r \).

Answer 1

The Correct Option is C

First, calculate the perimeter of the square: \[ \text{Perimeter of square} = 4 \times 11 = 44 \, \text{cm} \] Next, use the formula for the circumference of a circle: \[ C = 2 \pi r \] We are given that the circumference of the circle is equal to the perimeter of the square, so: \[ 2 \pi r = 44 \] Solving for \( r \): \[ r = \frac{44}{2 \pi} = \frac{22}{\pi} \] Now, calculate the area of the circle using the formula \( A = \pi r^2 \): \[ A = \pi \left( \frac{22}{\pi} \right)^2 = \frac{484}{\pi} \] Using \( \pi \approx 3.1416 \): \[ A \approx \frac{484}{3.1416} \approx 154 \, \text{cm}^2 \] Thus, the correct answer is 144 cm\(^2\).