Find the area of the unshaded region inside a circle of radius $10\text{ cm}$ surrounding a inscribed right isosceles triangle with hypotenuse as diameter.
Step-by-Step Solution
Key Concept: Circle area $= \pi(10)^2 = 100\pi = 314\text{ cm}^2$. Inscribed triangle base $= 20$, height $= 10 \Rightarrow \text{Area} = \dfrac{1}{2} \times 20 \times 10 = 100\text{ cm}^2$. Unshaded area $= 314 - 100 = 214\text{ cm}^2$.
Circle Area $= 3.14 \times 100 = 314\text{ cm}^2$. [1.0 Mark]
Triangle Area $= \dfrac{1}{2} \times 20 \times 10 = 100\text{ cm}^2$. [1.0 Mark]
Unshaded Area $= 314 - 100 = 214\text{ cm}^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Calculating circle area $= 314\text{ cm}^2$: 1.0 Mark
Calculating inscribed triangle area $= 100\text{ cm}^2$: 1.0 Mark
Evaluating difference $= 214\text{ cm}^2$: 1.0 Mark
Correct Answer: