SSC CGL 2025 Tier-I · 14 September 2025, Shift 1 · Quantitative Aptitude · Question 21 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A sector of a circle having a radius 14 cm has area 154 cm². Find the angle of the sector.

(a)90°
(b)120°
(c)150°
(d)180°

Answer

Why

Correct — A. A sector's area is the fraction θ⁄360 of the whole circle's area.

Whole circle: πr² = 22⁄7 × 14 × 14 = 616 cm²
Fraction the sector takes: 154 ÷ 616 = 1⁄4

Angle: 1⁄4 × 360° = 90° → option (a)

Why the others are wrong

(b)
120° — 120° is one-third of the circle, which would make the sector 616 ÷ 3 ≈ 205.3 cm², not 154 cm².
(c)
150° — A 150° sector is 5⁄12 of the circle: 5⁄12 × 616 ≈ 256.7 cm², well above the given 154 cm².
(d)
180° — 180° is a semicircle: half of 616 cm² is 308 cm², double the 154 cm² given.

Concept

A sector is a slice of the circle, so its area is the same fraction of πr² as its angle is of 360°: area = θ⁄360 × πr².

Reverse the formula to find the angle: θ = 360° × (sector area ÷ πr²). With r = 14 cm, πr² = 616 cm², and 154 is exactly a quarter of that, so the sector is a quadrant.

Key facts

Area of a sector = θ⁄360 × πr².
With π = 22⁄7, a circle of radius 14 cm has area 616 cm² and circumference 88 cm.
Arc length of a sector = θ⁄360 × 2πr, so this 90° sector has an arc of 88 ÷ 4 = 22 cm.

Study next

Arc length and perimeter of a sectorSector area from arc length: area = ½ × arc length × radiusArea of a segment: sector area minus triangle area

Common traps

Dividing by the circumference, 2πr = 88 cm, instead of the area πr² = 616 cm²: the ratio must compare area with area.
Treating 154 cm² as the whole circle: that is the area of a circle of radius 7 cm, not 14 cm.

The same angle-from-area reversal is asked at 17 Sep 2024, 09:00, Quant Q.12, where area 16π with radius 8 is 16π ÷ 64π = 1⁄4 of the circle, again 90°. At 19 Sep 2024, 16:00, Quant Q.8 the radius is the unknown: 462 cm² at 120° gives r = 21 cm.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 84 SSC CGL questions on it, every solved shift.