SSC CGL 2024 Tier-I · 25 September 2024, Shift 2 · Quantitative Aptitude · Question 8 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 10 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 14 cm, makes an angle of 45° at the centre. Find the perimeter (in cm) of the sector. (Use π = 22⁄7)

(a)38
(b)39
(c)34
(d)28

Answer

Why

Correct — B. The perimeter of a sector is the arc plus the two radii, never the arc alone.

Full circumference = 2 × 22⁄7 × 14 = 88 cm
Arc for 45° = (45⁄360) × 88 = (1⁄8) × 88 = 11 cm

Two radii = 2 × 14 = 28 cm

Perimeter = 28 + 11 = 39 cm → option (b)

Why the others are wrong

(a)
38 — 38 cm is one centimetre short, which means the arc was taken as 10 cm. A 45° arc is one-eighth of the 88 cm circumference, and that is 11.
(c)
34 — 34 cm is 28 + 6, so it under-measures the arc by 5 cm. An arc of 6 cm on this circle would answer to about 25°, not 45°.
(d)
28 — 28 cm is the two radii alone, with the curved edge left out. A sector perimeter always includes the arc, so 11 cm is still to be added.

Concept

A sector is bounded by two straight radii and one curved arc, so its perimeter is 2r + arc.

The arc is the fraction θ⁄360 of the whole circumference: arc = (θ⁄360) × 2πr.

Keep perimeter and area apart. The area of this sector is (θ⁄360) × πr² = (1⁄8) × (22⁄7) × 196 = 77 cm², a different quantity with different units.

Radius 14 with π = 22⁄7 is chosen so the sevens cancel: 2πr comes out at exactly 88, and 45° takes an eighth of it.

The stem is printed as an image in the response sheet. It reads: a circular arc whose radius is 14 cm makes an angle of 45° at the centre, find the perimeter of the sector, using π = 22⁄7.

Key facts

Perimeter of a sector = 2r + (θ⁄360) × 2πr.
With r = 14 and π = 22⁄7 the circumference is exactly 88 cm.
A 45° sector is one-eighth of the circle, so its arc is 11 cm and its perimeter 39 cm.

Study next

Area of a sector and length of an arc kept as separate formulaePerimeter of a segment, which replaces the two radii with a chordSector angles supplied in radians instead of degrees

Common traps

Reporting the arc length of 11 cm as the perimeter
Adding one radius instead of two
Using (θ⁄360) × πr² when the stem asks for a perimeter

SSC asks the same formula with the angle and the value of π switched, which decides whether the answer is exact or rounded. It is a 30° sector at 12 Sep 2024, 16:00, Quant Q.20, a 60° one at 18 Sep 2024, 09:00, Quant Q.4, and a 15° one at 17 Sep 2024, 16:00, Quant Q.7, where two decimal places are demanded.

Related PYQs

No directly related past PYQ was found.