Area of a segment of a circle of radius $r$ with central angle $90^\circ$ is:
(a) $\left(\dfrac{\pi}{4} - \dfrac{1}{2}\right) r^2$
(b) $\left(\dfrac{\pi}{2} - 1\right) r^2$
(c) $\left(\dfrac{\pi}{4} - 1\right) r^2$
(d) $\dfrac{\pi r^2}{4}$
Step-by-Step Solution
Key Concept: $\text{Area of sector} - \text{Area of } \Delta = \dfrac{\pi r^2}{4} - \dfrac{1}{2} r^2 = \left(\dfrac{\pi}{4} - \dfrac{1}{2}\right) r^2$.
$\text{Segment Area} = \dfrac{\pi r^2}{4} - \dfrac{1}{2}r^2 = \left(\dfrac{\pi}{4} - \dfrac{1}{2}\right) r^2$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $(\pi/4 - 1/2)r^2$: 1.0 Mark
Correct Answer: $\left(\dfrac{\pi}{4} - \dfrac{1}{2}\right) r^2$