SSC CHSL 2023 PYQ — Question 68

The correct answer is option 1 i.e. $49\sqrt{3}-77cm^{2}$.

Each side of equilateral triangle = r + r = 7 + 7 = 14 cm

Angle subtended by the sector in an equilateral triangle = 60°

Area of a sector of circle = (θ/360) × πr² = (60/360) × (22/7) × 7² ⇒ 77/3 cm²

Area of equilateral triangle = (√3/4) × 14² = 49√3 cm²

Area enclosed between circles = Area of a triangle - 3 (Area of the sector)

= 49√3 - 3(77/3)

= 49√3 - 77 cm²

Hence, the area enclosed between the circles is 49√3 - 77 cm².