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