Find the area of a quadrant of a circle whose circumference is $22\text{ cm}$.
Step-by-Step Solution
Key Concept: $2\pi r = 22 \Rightarrow r = 3.5\text{ cm}$. Area of quadrant $= \dfrac{1}{4} \pi r^2 = \dfrac{1}{4} \times \dfrac{22}{7} \times \dfrac{49}{4} = \dfrac{77}{8}\text{ cm}^2 = 9.625\text{ cm}^2$.
$2 \times \dfrac{22}{7} \times r = 22 \Rightarrow r = \dfrac{7}{2}\text{ cm}$. [1.0 Mark]
$\text{Area} = \dfrac{1}{4} \times \dfrac{22}{7} \times \dfrac{49}{4} = \dfrac{77}{8}\text{ cm}^2 = 9.625\text{ cm}^2$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Finding radius $r = 7/2\text{ cm}$: 1.0 Mark
Evaluating quadrant area $= 77/8\text{ cm}^2$: 1.0 Mark
Correct Answer: