SSC CGL 2024 Tier-I · 13 September 2024, Shift 2 · Quantitative Aptitude · Question 21 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 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.

What is the volume in cubic units of a cylinder with a height equal to the diameter and a radius is 4 units?

Answer

Why

Correct — C. Turn the sentence into two numbers first. The radius is 4, so the diameter is 8, and the question sets the height equal to that diameter.

r = 4
h = 2r = 8

V = πr²h = π × 4² × 8
= π × 16 × 8
= 128π cubic units → option (c)

Why the others are wrong

(a)
32π is πr²h with the height taken as 2 instead of 8. The stem sets height = diameter = 2 × 4, and the correct volume is four times this figure.
(b)
64π⁄3 carries a stray 1⁄3, and that factor belongs to a cone, V = 1⁄3 πr²h. It also uses h = 4, the radius, where the question asks for the diameter.
(d)
32π⁄3 compounds two errors: the cone's 1⁄3, which a cylinder does not have, and a height of 2 rather than the stated 8.

Concept

A cylinder's volume is πr²h — base area times height. The only real work here is translating "height equal to the diameter" into h = 2r.

That particular cylinder is worth knowing: h = 2r is the cylinder that exactly encloses a sphere of radius r, and its volume simplifies to πr²(2r) = 2πr³. With r = 4 that is 2π × 64 = 128π, a one-line check on the answer.

Archimedes' result sits on top of it: the enclosed sphere fills exactly two-thirds of that cylinder.

The options are all multiples of π, so the arithmetic stays exact and no value of π needs substituting. Two of the four carry a 1⁄3, which is the cone's factor — the question is quietly checking that you have not merged the two formulas.

Key facts

Volume of a cylinder = πr²h, and its curved surface area = 2πrh.
When the height equals the diameter, h = 2r and the volume becomes 2πr³.
A sphere occupies two-thirds of the volume of the cylinder that just encloses it, which is Archimedes' theorem.
With r = 4 and h = 8: π × 16 × 8 = 128π cubic units.

Study next

Curved and total surface area of a cylinder, and when each is askedSphere and hemisphere volumes, including the 2 : 3 sphere-to-cylinder ratioCone volume 1⁄3 πr²h and the cone-cylinder-sphere family

Common traps

Substituting the diameter 8 for the radius, which gives 512π.
Reaching for 1⁄3 πr²h, which is the cone.
Reading "height equal to the diameter" as height equal to the radius.

A cylinder item can hand you a surface area in place of the dimension you need.

On 12 Sep 2024, 09:00, Quant Q.14 the height is 20 cm and the lateral surface area 1760 cm². On 19 Sep 2024, 12:30, Quant Q.13 the radius is 10.5 cm and the curved surface area 792 cm², keyed 4158.

Both ask for the volume, so both run the same way: recover the missing dimension from the surface area, then apply πr²h.

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