SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · Quantitative Aptitude · Question 23 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 11 September 2026.

Where this paper and its answers come from

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 circular decorative wall clock with a radius of 20 cm has a design where a chord connects two points on the circumference. This chord, along with two radii, forms an equilateral triangle at the center of the clock face. The smaller segment created by this chord is painted in a contrasting color. What percentage of the clock's total area does this smaller painted segment represent? (Use π≈3.14, √3≈1.732)

(a)2.88%
(b)5.6%
(c)9.08%
(d)12.5%

Answer

Why

Correct — A. Two radii and the chord make an equilateral triangle, so the centre angle is 60°. The segment is the sector minus that triangle.

Sector: 60⁄360 × 3.14 × 20² = 1256 ÷ 6 = 209.33 cm²
Triangle: √3⁄4 × 20² = 0.433 × 400 = 173.2 cm²
Subtract: 209.33 − 173.2 = 36.13 cm²

Whole clock face: 3.14 × 20² = 1256 cm²
Share: 36.13 ÷ 1256 × 100 ≈ 2.88% → option (a)

Why the others are wrong

(b)
5.6% — 5.6% of the 1256 cm² face is about 70.3 cm², nearly double the 36.13 cm² that sector minus triangle leaves.
(c)
9.08% — 9.08% of 1256 cm² is about 114 cm², over three times the segment. Dividing 36.13 by r² = 400 instead of by πr² = 1256 lands near it, at 9.03%.
(d)
12.5% — 12.5% is 1⁄8 of the circle, the share of a 45° sector. The angle here is 60°, and even the whole 60° sector is only 1⁄6 ≈ 16.67% before the triangle comes off.

Concept

A segment is the region between a chord and its arc. Its area is the sector with the same central angle minus the triangle formed by the two radii and the chord.

With an equilateral triangle, the angle is 60°, the sector is 1⁄6 of the circle, and the triangle is (√3⁄4)r². As a share of the circle, the segment is 1⁄6 − √3⁄(4π) ≈ 0.0288, whatever the radius.

The chord splits the face into this small segment and a major segment of about 97.12%. The stem asks for the smaller one.

Key facts

Area of a sector = θ⁄360 × πr².
Area of an equilateral triangle of side a = (√3⁄4)a².
Minor segment for a 60° central angle = r²(π⁄6 − √3⁄4).

Study next

Segment area for a 90° angle, where the triangle is right-angled: r²(π⁄4 − 1⁄2)Area of the major segment, the circle minus the minor oneArea of an equilateral triangle from its side, height or inradius

Common traps

Stopping at the sector (209.33 cm², about 16.67% of the face) without subtracting the triangle.
Dividing the segment by r² instead of πr², which gives about 9.03%.
Taking the centre angle as 90°, when an equilateral triangle puts 60° there.

15 Sep 2025, 12:30, Quant Q.24 asks for the same 60° segment in exact form: r = 6 cm, keyed (6π−9√3) sq. cm.

10 Sep 2024, 09:00, Quant Q.23 turns the pieces round: 60° sectors are subtracted from an equilateral triangle of side 28 cm, keyed 31.08 cm².

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 84 SSC CGL questions on it, every solved shift.