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Class 10 › Mathematics › Areas Related to Circles
CBSE2026Class Class 10 · Mathematics1 Marks · Mcq✅ Verified
Area of a segment of a circle of radius 'r' and central angle $60^\circ$ is :
A. $\dfrac{\pi r^2}{2} - \dfrac12 r^2$
B. $\dfrac{2\pi r}{4} - \dfrac{\sqrt3}{4}r^2$
C. $\dfrac{\pi r^2}{6} - \dfrac{\sqrt3}{4}r^2$
D. $\dfrac{2\pi r}{4} - r^2\sin 60^\circ$
✅ Answer & Solution
✅ Correct Answer: C
**Step 1 — Recall the formula.**
$$\text{Area of segment} = \text{Area of sector} - \text{Area of triangle}$$
**Step 2 — Area of the sector for $\theta = 60^\circ$.**
$$= \frac{\theta}{360^\circ} \times \pi r^2 = \frac{60}{360}\pi r^2 = \frac{\pi r^2}{6}$$
**Step 3 — Area of the triangle.**
The two radii are equal and the included angle is $60^\circ$, so the triangle is **equilateral** with side $r$.
$$\text{Area} = \frac{\sqrt3}{4}r^2$$
