SSC CGL 2024 Tier-I · 19 September 2024, Shift 2 · Quantitative Aptitude · Question 13 of 99

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.

The base radius of a circular cylinder is 10.5 cm. If the area of its curved surface is 792 cm 2 , then what is the volume of the cylinder?

(a)4152 cm
(b)4158 cm
(c)4518 cm
(d)4185 cm

Answer

Why

Correct — B. The curved surface gives you the height first, and the height then gives the volume.

CSA = 2πrh, with r = 10.5 cm and π = 22⁄7
2 × 22⁄7 × 10.5 = 66
So 66h = 792 → h = 792 ÷ 66 = 12 cm

Volume = πr²h
= 22⁄7 × 10.5 × 10.5 × 12
= 33 × 10.5 × 12 = 346.5 × 12 = 4158 → option (b).

Why the others are wrong

(a)
4152 cm — Six short of the exact product. πr²h here is 346.5 × 12, which lands on 4158 with nothing to round; 4152 would need a height of about 11.98 cm, and 792 ÷ 66 divides exactly to 12.
(c)
4518 cm — Needs a taller cylinder. A volume of 4518 would require h ≈ 13.04 cm, but the curved surface pins the height at 12: 2 × (22⁄7) × 10.5 = 66, and 792 ÷ 66 = 12.
(d)
4185 cm — A transposition of 4158, its last two digits swapped. 4185 would mean a height of about 12.08 cm, while the height here comes out exactly 12.

Concept

Curved surface area is 2πrh — the label wrapped round the tin, with neither end included. It is linear in h, so a single division recovers the height.

Volume is πr²h, where the r appears squared. That difference is the whole question: the CSA hands you h, and only then does r² come into play.

The radius 10.5 is chosen so that 22⁄7 cancels — 10.5 ÷ 7 = 1.5 exactly. Radii of 3.5, 7, 10.5, 14 and 21 all do this, and spotting it removes the decimals from the arithmetic.

All four options are printed with the unit cm although a volume is measured in cm³, and the stem prints the area as "792 cm 2". Both are typographic faults in the paper and neither affects which option is keyed.

Key facts

Curved (lateral) surface area of a cylinder is 2πrh, excluding the two circular ends.
Total surface area adds those ends: 2πr(h + r).
With r = 10.5 cm and π = 22⁄7, the factor 2πr equals 66, so the curved surface is simply 66h.
Volume of a cylinder is πr²h, which for these values is 346.5 × 12 = 4158 cm³.

Study next

Total surface area of a cylinder against its curved surface areaRadii picked as multiples of 3.5 so that 22⁄7 cancels cleanlyCurved surface area of a cone, πrl, where the slant height replaces the height

Common traps

Using 2πr(h + r) when the stem says curved surface, which makes the height come out too small
Halving twice — writing r = 10.5 and then treating 10.5 as the diameter
Doubting a correct 4158 because the options print cm where cm³ belongs

The surface measure is the way in, not the answer: the formula you are handed is 2πrh and the one you need is πr²h.

13 Sep 2024, 16:00, Quant Q.2 gives a cylinder with a curved surface of 880 cm² and asks for the product of its height and radius — the same 2πrh, rearranged one step earlier than here.

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