A sector has a central angle of 180°and a radius of 12 cm. Another sector has a central angle of (π)/2 radians and the same radius. What is the ratio of the area of the first sector to the area of the second sector?

A sector has a central angle of 180°and a radius of 12 cm…

A sector has a central angle of 180°and a radius of 12 cm. Another sector has a central angle of $\frac{\pi}{2}$ radians and the same radius. What is the ratio of the area of the first sector to the area of the second sector?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 2 : 1.

Area of sector (for degrees) $=\frac{\theta}{360^\circ} \times \pi r^2$

Area (for radians) $= \frac{\theta}{2\pi} \times \pi r^2$

Area of first sector = (180/360) × π × 12² = (1/2) × 144π = 72π

Area of second sector = (π/2)/2π × π × 12² = (1/4) × 144π = 36π

Ratio = 72π : 36π = 2 : 1

SSC CGL 2025 PYQ — Question 59