Find the area of a circle whose circumference is equal to the perimeter of a square of side $11\text{ cm}$.
Step-by-Step Solution
Key Concept: Square perimeter $= 4 \times 11 = 44\text{ cm}$. Circumference $= 2 \times \dfrac{22}{7} \times r = 44 \Rightarrow r = 7\text{ cm}$. Area $= \dfrac{22}{7} \times 49 = 154\text{ cm}^2$.
$2\pi r = 44 \Rightarrow r = 7\text{ cm}$. [1.0 Mark]
$\text{Area} = \dfrac{22}{7} \times 49 = 154\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Finding radius $r = 7\text{ cm}$: 1.0 Mark
Evaluating area $= 154\text{ cm}^2$: 1.0 Mark
Correct Answer: