SSC CGL 2024 Tier-I · 18 September 2024, Shift 1 · Quantitative Aptitude · Question 4 of 99

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.

A circular arc whose radius is 24 cm makes an angle of 60° at the centre. The perimeter of the sector formed is: (Use π = 3.14)

(a)73.22 cm
(b)63.12 cm
(c)73.12 cm
(d)74.32 cm

Answer

Why

Correct — c. The perimeter of a sector is the arc plus the two radii that bound it, so both parts have to be found.

Arc = (θ⁄360) × 2πr
= (60⁄360) × 2 × 3.14 × 24
= (1⁄6) × 150.72 = 25.12 cm

Two radii = 2 × 24 = 48 cm

Perimeter = 25.12 + 48 = 73.12 cm → option (c).

Why the others are wrong

(a)
73.22 cm — 73.22 needs an arc of 25.22 cm. The arc is (1⁄6) × 2 × 3.14 × 24 = 25.12, so the second decimal is a 1, not a 2 — these options separate on that digit.
(b)
63.12 cm — 63.12 is 25.12 + 38. A sector is closed by two radii of 24 cm, so the straight part of the boundary is 48 cm.
(d)
74.32 cm — 74.32 needs an arc of 26.32 cm. The arc here is exactly 8π, and the paper's π = 3.14 makes that 25.12 cm.

Concept

Two different lengths hide behind the word 'perimeter' in this question.

The arc is the curved part alone: (θ⁄360) of the circumference 2πr. At 60° that is one sixth of the circle, which is 8π here.

The perimeter of the sector closes the shape, so it adds the two radii running from the centre to the ends of the arc: perimeter = arc + 2r.

A question asking for arc length alone would answer 25.12 cm. This one asks for the boundary of the slice, so 48 cm of straight edge goes in as well.

The paper supplies π = 3.14, so the answer is a two-decimal number rather than a multiple of π. Three of the four options lie within 1.2 cm of each other, which makes the decimals worth carrying.

Key facts

Arc length of a sector = (θ⁄360) × 2πr.
Perimeter of a sector = arc length + 2r, because two radii bound the slice.
With r = 24 and θ = 60°, the arc is 8π = 25.12 cm and 2r = 48 cm.

Study next

Area of a sector, (θ⁄360) × πr², and why it is not the perimeterThe chord joining the arc's ends, and how it differs from the arcSector problems stated in radians rather than degrees

Common traps

Stopping at the arc and choosing whichever option sits near 25
Adding one radius instead of two
Reaching for π = 22⁄7 out of habit when the paper prints π = 3.14

SSC reuses this formula with the numbers changed: 12 Sep 2024, 16:00, Quant Q.20 gives a 12 cm radius and 30°, and its key is 30.28 cm — that is 6.28 of arc plus 24 of radii. Recognising 'perimeter of the sector' as arc + 2r is the whole question in both.

Related PYQs

No directly related past PYQ was found.