SSC CGL 2024 Tier-I · 9 September 2024, Shift 2 · Quantitative Aptitude · Question 19 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 5 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.

From a circle with the radius of 15.75 cm, a sector with the arc length of 11 cm is cut off. Find the area (in cm 2 ) of this sector.

(a)86.625
(b)86.875
(c)86.525
(d)86.125

Answer

Why

Correct — A. Area and arc are the same fraction θ/360° of the circle, so the angle cancels when you divide one by the other.

area = (θ/360°) × πr² and arc l = (θ/360°) × 2πr
area ÷ l = r/2, so area = ½ × r × l

Substitute r = 15.75 cm and l = 11 cm:
area = ½ × 15.75 × 11
= 173.25 ÷ 2 = 86.625 cm² → option (a)

No value of π and no central angle are needed.

Why the others are wrong

(b)
86.875 — Fails the reverse check: 2 × area ÷ arc must give back the radius. 86.875 doubles to 173.75, and 173.75 ÷ 11 = 15.80 cm, not the given 15.75 cm — a carry slip in 15.75 × 11.
(c)
86.525 — Same check, same failure: 86.525 doubles to 173.05, and 173.05 ÷ 11 ≈ 15.73 cm. The circle's radius is 15.75 cm, so the multiplication has lost 0.02 of a unit somewhere.
(d)
86.125 — 86.125 doubles to 172.25, implying a radius of about 15.66 cm. The arc has been used correctly — it is the product 15.75 × 11 = 173.25 that has gone wrong.

Concept

A sector is the fraction θ/360 of a whole circle, so its area is that fraction of πr² and its arc is the same fraction of 2πr.

Because the fraction is shared, dividing one by the other kills both θ and π and leaves area = ½ r l.

It is the circular twin of ½ × base × height, with the arc as the base and the radius as the height, and it holds for any sector provided r and l are in the same unit.

Whenever a question hands you the arc instead of the angle, this is the one-line route.

The numbers are built for π = 22/7: the circumference is 2 × (22/7) × 15.75 = 99 cm.

An 11 cm arc is therefore exactly 11/99 = 1/9 of the circle, a central angle of 40°. You never need that to answer, but it confirms the figures are consistent.

Key facts

Sector area = ½ × radius × arc length, with radius and arc in the same unit.
Sector area = (θ/360°) × πr², and arc length = (θ/360°) × 2πr.
Here ½ × 15.75 × 11 = 86.625 cm², and π never enters the calculation.
The sector's central angle is 40°, since 11 cm is one-ninth of the 99 cm circumference.

Study next

Arc length and sector area from a given central angle, in degrees and in radiansSegment area = sector area − the triangle formed by the two radii and the chordPerimeter of a sector = arc + 2r, the usual follow-up on the same figure

Common traps

Reaching for (θ/360) × πr² and hunting for θ, when ½rl needs no angle at all.
Using the sector's perimeter, 11 + 2 × 15.75, in place of the arc length.
Rounding 15.75 to 15.8 early — the four options are separated by as little as 0.1.

SSC supplies two of the three quantities — radius, arc, central angle — and asks for area or perimeter.

When the arc is one of the two given, ½rl is the intended route, and the radius is chosen so that π = 22/7 cancels cleanly.

Related PYQs

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