SSC CGL 2024 Tier-I · 9 September 2024, Shift 3 · Quantitative Aptitude · Question 7 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.

What is the perimeter (in cm, rounded off to one decimal place) of the sector of a circle with a radius of 10 cm and of angle 30°? (Use π = 3.14)

(a)82.8
(b)25.2
(c)20.4
(d)35.7

Answer

Why

Correct — B. The perimeter of a sector is the arc plus the two radii — a sector is a closed pie slice, not just a curve.

Arc length = (θ⁄360) × 2πr
= (30⁄360) × 2 × 3.14 × 10
= (1⁄12) × 62.8 = 5.233 cm

Two radii = 2 × 10 = 20 cm

Perimeter = 20 + 5.233 = 25.233
Rounded to one decimal place: 25.2 cm → option (b).

Why the others are wrong

(a)
82.8 — This is the whole circle plus the two radii: 62.8 + 20 = 82.8. The sector uses only 30⁄360, a twelfth, of that circumference.
(c)
20.4 — Barely more than the two radii alone (20 cm), so it leaves out most of the arc. The arc contributes 5.23 cm, which lifts the perimeter to 25.2.
(d)
35.7 — Too large. Subtracting the two radii leaves an arc of 15.7 cm, which is a quarter of the circumference — that is the 90° sector, not the 30° one the stem gives.

Concept

A sector is a pie slice bounded by two radii and one arc.

Its perimeter is 2r + arc, and the arc is the fraction θ⁄360 of the full circumference 2πr. With θ = 30° that fraction is 1⁄12.

Area uses the same fraction on a different formula: (30⁄360) × πr² = (1⁄12) × 3.14 × 100 = 26.17 cm². Perimeter and area differ only in what the fraction multiplies, so read which one the stem wants.

The two radii are the piece candidates drop, because "perimeter" in most figures means a single closed curve.

The stem prescribes π = 3.14 and asks for one decimal place, which fixes the answer exactly — a candidate using 22⁄7 gets 25.238, still 25.2 to one decimal, so the rounding instruction matters more than the choice of π here.

Key facts

Perimeter of a sector = 2r + (θ⁄360) × 2πr.
Area of a sector = (θ⁄360) × πr².
With r = 10 cm, θ = 30° and π = 3.14, the arc is 5.23 cm and the perimeter is 25.2 cm.
Arc length also equals rθ when θ is measured in radians rather than degrees.

Study next

Area of a sector and the area of a segment cut off by a chordArc length in radians, written as l = rθPerimeter of a semicircle and of a quadrant, where the straight parts are easy to miss

Common traps

Reporting the arc length alone and forgetting the two radii.
Using the full circumference in place of the 30⁄360 fraction of it.
Rounding 5.233 to 5 before adding, which destroys the first decimal place.

The angle is kept to a friendly fraction of 360 — 30°, 45°, 60° or 90° — and π is prescribed in the stem so every candidate should land on the same decimal.

Quant Q.10 runs the same sector formula backwards — perimeter 64⁄3 cm, angle 60°, find the area. Mensuration also appears at Quant Q.21 (area of congruent triangles) and Quant Q.25 (volume of a cuboid).

Related PYQs

No directly related past PYQ was found.