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SSC CGL 2025 PYQ — Question 51

SSC CGL - 12 Sep 2025 - Shift 3 • Quantitative Aptitude • Q51

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A sector of a circle has a central angle of 90° and a radius of 10 cm. Another sector of the same circle has a central angle of 3π/4 radians. What is the ratio of the area of the first sector to the area of the second sector?

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 2 : 3.

Area of sector = θ360×πr2{\theta \over 360} \times \pi r^2

Area of first sector = 90360×π×102{90 \over 360} \times \pi \times 10^2

⇒ 100π/4 = 25π

Now, angle of second sector in degrees = 3 × 180/4 = 135°

Area of second sector = 135360×π×102{135 \over 360} \times \pi \times 10^2

⇒ 37.5π

Required ratio = 25π : 37.5π

⇒ 250 : 375 

⇒ 10 : 15 = 2 : 3