SSC CGL 2024 Tier-I · 9 September 2024, Shift 3 · Quantitative Aptitude · Question 10 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.

Find the area (in cm²) of the sector whose perimeter is 64⁄3 cm and central angle is 60°. (Use π = 22⁄7.)

Answer

Why

Correct — D. A sector is fenced in by two radii plus the arc, so its perimeter is 2r + (60/360) × 2πr, not the arc alone.

Perimeter = 2r + (1/6) × 2 × (22/7) × r
= 2r + 22r/21 = 64r/21
64r/21 = 64/3 → r = 7 cm

Area = (60/360) × πr² = (1/6) × (22/7) × 49
= 154/6 = 77/3 cm² → option (d)

Why the others are wrong

(a)
47/3 ≈ 15.7 cm² is well under the true area. It would need a radius near 5.5 cm, and the perimeter equation 64r/21 = 64/3 has the single solution r = 7 cm.
(b)
85/3 ≈ 28.3 cm² is the largest option and needs r ≈ 7.35 cm — a sector perimeter of about 22.4 cm, not the 64/3 ≈ 21.33 cm the question gives.
(c)
68/3 ≈ 22.7 cm² corresponds to a radius near 6.6 cm. Solve the perimeter first and r is pinned at exactly 7, so no rounding of the radius reaches this value.

Concept

A sector is bounded by two radii and an arc, so perimeter = 2r + (θ/360) × 2πr. Leaving the 2r out is the single commonest error in this family.

Perimeter and area both carry the same factor θ/360, so SSC can hand you either and ask for the other; the radius is the bridge between them.

At θ = 60° the arc is one-sixth of the circumference and the sector one-sixth of the circle, which is why the working collapses to r(2 + 22/21) and then (11/21)r².

The stem is printed as an image. It reads: "Find the area (in cm²) of the sector whose perimeter is 64/3 cm and central angle is 60°. (Use π = 22/7.)"

All four options are images too, reading 47/3, 85/3, 68/3 and 77/3.

Key facts

Perimeter of a sector = 2r + (θ/360) × 2πr — two radii plus the arc.
Area of a sector = (θ/360) × πr², which also equals (1/2) × arc length × r.
At θ = 60° the arc and the area are each exactly one-sixth of the whole circle's.
With π = 22/7 and r = 7 cm the numbers stay whole: circumference 44 cm, full area 154 cm².

Study next

Arc length and sector area for a given central angle, in both degrees and radiansArea of a segment, found as the sector's area minus the triangle'sPerimeter and area of a semicircle and of a quadrant

Common traps

Using the arc alone as the perimeter, which drops the 2r and inflates the radius.
Switching π between 22/7 and 3.14 mid-question, after which r stops being a whole 7.
Finding r correctly and then reporting the full circle's 154 cm² instead of its sixth.

This shift runs the same formula the other way in Quant Q.7, which gives radius 10 cm and angle 30° and asks for the perimeter. Expect SSC to supply any two of radius, angle, perimeter and area and ask for a third.

Related PYQs

No directly related past PYQ was found.