SSC CGL 2024 Tier-I · 17 September 2024, Shift 1 · Quantitative Aptitude · Question 12 of 98

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the measure of the central angle of a sector if its area is 16π and the radius is 8.

(a)90°
(b)75°
(c)60°
(d)108°

Answer

Why

Correct — A. A sector is the fraction θ⁄360 of its circle, so sector area = (θ⁄360) × πr².

Whole circle: πr² = π × 8² = 64π
Set it equal to the given area: (θ⁄360) × 64π = 16π
Cancel π and divide: θ⁄360 = 16⁄64 = 1⁄4

θ = 360 × 1⁄4 = 90° → option (a).

Why the others are wrong

(b)
75° — 75° is 5⁄24 of the circle, giving 64π × 5⁄24 = 40π⁄3 ≈ 13.3π. The stem asks for 16π, and 16 : 64 is a clean quarter.
(c)
60° — 60° is one sixth of the circle: 64π ÷ 6 = 32π⁄3 ≈ 10.7π, well under the given 16π. Sixths come from a 60° reflex habit, not from this ratio.
(d)
108° — 108° is 3⁄10 of the circle: 64π × 3⁄10 = 19.2π, above the stated 16π. The ratio 16 : 64 fixes the fraction at a quarter, not three-tenths.

Concept

Every sector formula is the whole-circle formula scaled by θ⁄360.

Area = (θ⁄360) × πr², arc length = (θ⁄360) × 2πr. Both use the same fraction, which is why a question that gives you an area can be answered without ever finding an arc.

Here you are not really computing an area at all — you are comparing two areas. 16π against 64π is 1 : 4, and a quarter of 360° is 90°. Recognising the ratio saves the whole rearrangement.

The area is given as a multiple of π, so π cancels and no value of 22⁄7 or 3.14 is ever needed. Carrying a decimal for π here only introduces rounding error.

Key facts

Sector area = (θ⁄360) × πr² and arc length = (θ⁄360) × 2πr, both scaled by the same fraction θ⁄360.
A circle of radius 8 has area 64π, so a 16π sector is exactly one quarter of it.
A quarter of a circle subtends 90° at the centre.

Study next

Perimeter of a sector, which adds the two radii to the arcArea of a segment, found as the sector minus the triangleConverting a central angle between degrees and radians

Common traps

Using the arc-length formula when the stem gives an area.
Squaring the radius as 16 instead of 64, which inverts the fraction.
Substituting 22⁄7 for π when both sides already carry π and it cancels.

SSC gives two of {area, arc length, radius, angle} and asks for a third, often inverting the formula so the radius is the unknown.

The same sector relation is asked 17 Sep 2024, 09:00, Quant Q.24 (arc length equal to half the circumference), 10 Sep 2024, 16:00, Quant Q.17 (area and perimeter given, radius an integer) and 26 Sep 2024, 12:30, Quant Q.18 (an 80° sector of arc 96π, radius asked).

Related PYQs

No directly related past PYQ was found.