SSC CGL 2024 Tier-I · 12 September 2024, Shift 3 · Quantitative Aptitude · Question 20 of 100

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 12 cm makes an angle of 30° at the centre. Find the perimeter (in cm) of the sector formed. (Use π = 3.14)

(a)32.38
(b)30.28
(c)28.64
(d)26.24

Answer

Why

Correct — B. The perimeter of a sector is the arc plus the two radii that close it, not the arc on its own.

Arc = (30⁄360) × 2πr = (1⁄12) × 2 × 3.14 × 12
= 6.28 cm
Two radii = 2 × 12 = 24 cm
Perimeter = 24 + 6.28 = 30.28 cm

That is option (b).

Why the others are wrong

(a)
32.38 — Take away the 24 cm of radii and 32.38 leaves 8.38 cm of arc, which is what a sector of about 40° measures on this radius, not one of 30°.
(c)
28.64 — 28.64 leaves only 4.64 cm for the arc. A 30° arc is a twelfth of the 75.36 cm circumference, which comes to 6.28 cm.
(d)
26.24 — 26.24 leaves just 2.24 cm of arc after the two radii — little more than a third of the 6.28 cm a 30° arc actually measures here.

Concept

A sector has three edges: two radii and the arc between them. Its perimeter adds all three, while its area is (θ⁄360) × πr². Reaching for the area formula when a length is wanted is the usual failure on this shape.

The arc itself is the fraction θ⁄360 of the full circumference 2πr. At 30° that fraction is 1⁄12, so the arc is one twelfth of 75.36 cm.

The paper supplies π = 3.14, which is why the answer is a decimal rather than an expression in π. Use the value given rather than 22⁄7.

The wording asks for the perimeter of the sector formed, so the two straight edges belong to the boundary. A question wanting only the curved edge would have 6.28 cm as its answer.

Key facts

Perimeter of a sector = 2r + (θ⁄360) × 2πr.
Area of a sector = (θ⁄360) × πr², a formula for area and not for length.
With r = 12 and π = 3.14 the full circumference is 75.36 cm.
A 30° sector is one twelfth of the circle, because 360 ÷ 30 = 12.

Study next

Area of a sector and of the segment its chord cuts offLength of a chord and the perpendicular distance from the centreArc length in radians, where the arc is simply rθ

Common traps

Answering 6.28 cm, the arc alone, and forgetting that a perimeter has to close the figure.
Using the area formula instead, which here gives 37.68 and is not a length at all.
Substituting 22⁄7 when the paper has fixed π = 3.14, which shifts the last decimal.

The angle and the value of π are chosen so the arithmetic stays mental, and the marks turn on whether you add the radii. The same sector geometry returns in symbolic form at 12 Sep 2024, 16:00, Quant Q.25, where the arc is wanted as a multiple of π.

Related PYQs

No directly related past PYQ was found.