SSC CGL 2024 Tier-I · 17 September 2024, Shift 2 · Quantitative Aptitude · Question 9 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 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.

If the height and diameter of a cylinder are 12 cm and 28 cm, respectively, then find the ratio of the total surface area to the curved surface area.

(a)13 : 6
(b)10 : 3
(c)13 : 5
(d)11 : 6

Answer

Why

Correct — A. Diameter 28 cm means radius r = 14 cm, with h = 12 cm.

CSA = 2πrh
TSA = 2πrh + 2πr² = 2πr(h + r)

Divide TSA by CSA and the common factor 2πr goes:
TSA : CSA = (h + r) : h
= (12 + 14) : 12
= 26 : 12 = 13 : 6 → option (a)

Why the others are wrong

(b)
10 : 3 — 10 : 3 is (12 + 28) : 12 — the diameter used where the radius belongs. Halving 28 to 14 is the entire first step of this question.
(c)
13 : 5 — 13 : 5 keeps the right first number but not the right pair. The ratio is (h + r) : h = 26 : 12, and reaching 13 : 5 with h = 12 would need a radius of 19.2 cm.
(d)
11 : 6 — 11 : 6 is 22 : 12, so it needs h + r = 22 and therefore a radius of 10 cm. The radius here is 14 cm, which gives 26 : 12.

Concept

For a right circular cylinder of radius r and height h:

CSA, the curved side alone = 2πrh
TSA, the side plus both circular ends = 2πrh + 2πr² = 2πr(h + r)

Dividing removes the common factor 2πr and leaves (h + r) : h. Because π disappears, the question can be finished without ever writing 22/7.

The only real work is turning the given diameter of 28 cm into a radius of 14 cm.

TSA here means the closed cylinder, both ends included.

If a stem says open at one end, the total surface area is 2πrh + πr² and the ratio becomes (2h + r) : 2h instead — worth reading the wording for.

Key facts

Curved surface area of a cylinder = 2πrh.
Total surface area of a closed cylinder = 2πr(h + r).
TSA : CSA for a closed cylinder simplifies to (h + r) : h, with π cancelling out.
Here r = 14 cm and h = 12 cm, so the ratio is 26 : 12 = 13 : 6.

Study next

Volume of a cylinder and the ratio questions built on πr²hSurface areas of a cone, where slant height replaces height in the curved formulaCylinders compared through ratios of radii and heights rather than absolute values

Common traps

Treating the given 28 cm as the radius rather than the diameter
Adding only one circular end, which is the open-cylinder formula
Substituting π = 22/7 and computing both areas in full, which costs time and invites slips

SSC sets the cylinder either as a ratio like this one, where π cancels, or as a numeric area.

A curved surface area of 880 cm² with the product of height and radius asked runs at 13 Sep 2024, 16:00, Quant Q.2, and two cylinders compared by ratios of radii and heights are set at 12 Sep 2024, 12:30, Quant Q.19.

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