SSC CGL 2024 Tier-I · 13 September 2024, Shift 1 · Quantitative Aptitude · Question 24 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 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.

One-quarter of a circular pizza of radius 21 cm was removed from the whole pizza. What is the perimeter (in cm) of the remaining pizza? (Use

(a)99
(b)128
(c)141
(d)131

Answer

Why

Correct — C. What remains is a three-quarter sector, and its boundary is the long arc plus the two radii the cut exposes.

Full circumference = 2πr = 2 × 22⁄7 × 21 = 132 cm
Arc of the remaining three quarters = 3⁄4 × 132 = 99 cm
Two straight edges created by the cut = 2 × 21 = 42 cm

Perimeter = 99 + 42 = 141 cm → option (c).

Why the others are wrong

(a)
99 — 99 cm is the arc alone. Taking a quarter out exposes two radii of 21 cm each, and those straight edges are part of the boundary of what is left on the plate.
(b)
128 — 128 cm matches no edge of this figure. The arc is 99, the two radii add 42, and the whole circumference is 132 — no combination of them reaches 128.
(d)
131 — 131 cm sits just under the whole circumference, 132 cm, which is the perimeter of an uncut pizza — and an uncut pizza has neither the shortened arc nor the two straight edges.

Concept

The perimeter of a sector is arc + 2r, not the arc by itself. Cutting a slice out of a circle removes part of the arc but adds two straight edges, so the boundary changes shape as well as length.

Here r = 21 is chosen so that 22⁄7 cancels cleanly: 2 × 22⁄7 × 21 = 132 exactly. Three quarters of 132 is 99, and the two exposed radii contribute 42.

Note the direction of the effect: removing a quarter increases the perimeter from 132 cm to 141 cm, while the area falls to three quarters of what it was.

No diagram is supplied with this question. The attached image carries only the tail of the stem that the text run cuts off — the instruction to use π = 22⁄7 — so the shape has to be read off the wording alone.

Key facts

Perimeter of a sector = arc length + 2r.
With r = 21 cm and π = 22⁄7, the full circumference is exactly 132 cm.
The three-quarter arc measures 99 cm and the two exposed radii add 42 cm, giving 141 cm.
Removing a quarter cuts the area to three quarters but raises the perimeter from 132 cm to 141 cm.

Study next

Perimeter and area of a sector for a stated central angleArc length from a central angle, l = (θ ⁄ 360) × 2πrPerimeter of composite figures built from arcs and straight edges

Common traps

Answering 99 cm, the arc, and forgetting the two radii the cut exposes.
Working with the quarter that was removed rather than the three quarters that remain, which gives 33 + 42 = 75 cm.
Carrying the area habit across, where a removed quarter does reduce the answer.

SSC picks radii that are multiples of 7 so 22⁄7 cancels, which is the signal that the intended route is arithmetic rather than a calculator. Circle work also appears at Quant Q.3 of the 13 Sep 2024, 09:00 paper, where a chord of 7 units cuts an arc from a circle of radius 7.

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