SSC CGL 2025 Tier-I · 17 September 2025, Shift 3 · Quantitative Aptitude · Question 11 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 hemisphere and cylinder of equal radii have equal total surface areas. Find the ratio of cylinder height to radius.

(a)1:2
(b)7:4
(c)6:5
(d)2:5

Answer

Why

Correct — A.
Hemisphere TSA = curved 2πr² + flat base πr² = 3πr²
Cylinder TSA = 2πr² + 2πrh = 2πr(r + h)
Set equal: 2πr² + 2πrh = 3πr²

Subtract 2πr²: 2πrh = πr²
Divide by 2πr: h = r⁄2
So height : radius = 1 : 2 → option (a)

Why the others are wrong

(b)
7:4 — 7 : 4 means h = 7r⁄4. The cylinder's TSA would be 2πr² + 3.5πr² = 5.5πr², far above the hemisphere's 3πr².
(c)
6:5 — 6 : 5 means h = 6r⁄5, giving a cylinder TSA of 2πr² + 2.4πr² = 4.4πr², not 3πr².
(d)
2:5 — 2 : 5 comes close but misses: h = 2r⁄5 gives 2πr² + 0.8πr² = 2.8πr², short of 3πr². The curved side must supply exactly πr², which needs h = r⁄2.

Concept

Total surface area counts every face. A solid hemisphere has its curved dome (2πr², half a sphere's 4πr²) plus the flat circle it sits on (πr²): 3πr².

A closed cylinder has two circular ends (2πr²) plus the curved side (2πrh). With the radii equal, the ends already supply 2πr², so the curved side must supply the missing πr².

The radius is not given and not needed: every term carries r, and the ratio h : r is what survives.

Key facts

TSA of a solid hemisphere = 3πr² (curved 2πr² + base πr²).
TSA of a closed cylinder = 2πr(r + h).
Curved surface area of a cylinder = 2πrh.

Study next

Curved vs total surface area of a hemisphere (2πr² vs 3πr²)Surface area of a cylinder capped with a hemisphere (composite solid)Cylinder and hemisphere of the same radius with equal volumes: h = 2r⁄3

Common traps

Using the hemisphere's curved area 2πr² alone: then 2πrh = 0, which no cylinder satisfies.
Using the cylinder's curved area 2πrh alone: 2πrh = 3πr² gives h : r = 3 : 2, which is not offered.
Answering radius : height (2 : 1) when the question asks height : radius.

Hemisphere TSA 3πr² also decides 18 Sep 2025, 12:30, Quant Q.11, where two hemispheres of radii 2 cm and 4 cm are recast into one (keyed ≈ 163 cm²).

Cylinder TSA 2πr(r + h) drives 17 Sep 2024, 12:30, Quant Q.9, the ratio of total to curved surface for height 12 cm and diameter 28 cm (keyed 13 : 6).

Related PYQs

No directly related past PYQ was found.

Topic: Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base — all 51 SSC CGL questions on it, every solved shift.