The area of a circle that can be inscribed in a square of side $6\text{ cm}$ is:
(a) $9 \pi\text{ cm}^2$
(b) $36 \pi\text{ cm}^2$
(c) $12 \pi\text{ cm}^2$
(d) $18 \pi\text{ cm}^2$
Step-by-Step Solution
Key Concept: Diameter of inscribed circle $=$ Side of square $= 6\text{ cm} \Rightarrow r = 3\text{ cm}$. Area $= \pi(3)^2 = 9\pi\text{ cm}^2$.
$r = 3\text{ cm} \Rightarrow \text{Area} = \pi(3)^2 = 9\pi\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating area $= 9\pi\text{ cm}^2$: 1.0 Mark
Correct Answer: $9 \pi\text{ cm}^2$