SSC CGL 2025 Tier-I · 24 September 2025, Shift 2 · Quantitative Aptitude · Question 19 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

A sector of a circle having a radius of 10 cm and has a central angle of 3π⁄4 radians. What is the area of the sector?

(a)30π cm²
(b)37.5π cm²
(c)45π cm²
(d)75π cm²

Answer

Why

Correct — B. The angle is in radians, so sector area = ½ r² θ.

Square the radius: r² = 10² = 100
Multiply by the angle: 100 × 3π⁄4 = 75π
Halve: 75π ÷ 2 = 37.5π

Check in degrees: 3π⁄4 radians = 135°, and 135⁄360 × π × 10² = 3⁄8 × 100π = 37.5π cm² → option (b)

Why the others are wrong

(a)
30π cm² — 30π cm² is 3⁄10 of the full circle (100π cm²). A 135° sector is 3⁄8 of the circle, and 3⁄8 × 100π = 37.5π.
(c)
45π cm² — 45π cm² is 9⁄20 of the circle, a sector of 162°. The given angle, 3π⁄4 radians, is 135°, which gives 37.5π.
(d)
75π cm² — 75π cm² is r²θ with the ½ left out. The radian formula is ½ r² θ, so 100 × 3π⁄4 = 75π must still be halved.

Concept

A sector's area is the fraction of a full turn it covers, times the circle's area πr².

In degrees: area = (θ⁄360°) × πr²
In radians: area = (θ⁄2π) × πr² = ½ r² θ

The radian form takes θ exactly as given, so 3π⁄4 goes straight in with no conversion.

The options keep π as a symbol, so no value of π such as 22⁄7 or 3.14 is needed. Only the ½ and the radian unit have to be handled.

Key facts

Sector area = ½ r² θ, with θ in radians.
Sector area = (θ⁄360°) × πr², with θ in degrees.
π radians = 180°, so 3π⁄4 radians = 135°.
Arc length = rθ, so sector area also equals ½ × arc length × r.

Study next

Arc length rθ and sector perimeter 2r + rθArea of a segment: sector area minus ½ r² sin θConverting degrees to radians: multiply by π⁄180

Common traps

Dropping the ½ in ½ r² θ. That doubles the area to 75π, one of the listed values.
Reading 3π⁄4 as degrees. The stem says radians, and 3π⁄4 radians is 135°.

23 Sep 2025, 16:00, Quant Q.19 asks the same with θ = π⁄4 radians and r = 8 cm: ½ × 64 × π⁄4 = 8π cm².

13 Sep 2025, 16:00, Quant Q.25 sets a 135° sector against a 3π⁄4-radian sector of the same circle and keys the ratio 1 : 1, because the two angles are equal.

Related PYQs

No directly related past PYQ was found.

Topic: Circle and its chords, tangents, angles subtended by chords of a circle, common tangents to two or more circles — all 140 SSC CGL questions on it, every solved shift.