SSC CGL 2025 PYQ — Question 38

The correct answer is option 2 i.e.  $(24\pi - 36\sqrt{3})$ sq. cm.

Radius (r) = 12 cm

Chord = 2rsin(θ/2)

⇒ 12 = 2 × 12 × sin(θ/2)

⇒ sin(θ/2) = 0.5

⇒ θ/2 = 30°

⇒ θ = 60°

Area of sector = (θ/360)πr² = (60/360)π × 12² = (1/6) × 144π = 24π cm²

Area of triangle = (1/2)r²sin θ = (1/2) × 12² × sin 60° = 72 × (√3/2) = 36√3 cm²

Minor segment = Sector area – Triangle area = (24π – 36√3) cm²