SSC CGL 2025 Tier-I · 24 September 2025, Shift 2 · General Intelligence and Reasoning · Question 18 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 13 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 cone and a cylinder have the same base radius and the same height. What is the ratio of the volume of the cone to the volume of the cylinder?

(a)1:2
(b)1:3
(c)1:4
(d)1:6

Answer

Why

Correct — B.
Rule: a cone holds one-third of the cylinder with the same base and height.

Cone: V = (1⁄3)πr²h
Cylinder: V = πr²h

Ratio = (1⁄3)πr²h : πr²h
Cancel πr²h → 1⁄3 : 1 = 1 : 3 → option (b).

Why the others are wrong

(a)
1:2 — 1 : 2 would make the cone half the cylinder. The cone formula carries 1⁄3, not 1⁄2, so the ratio is 1 : 3.
(c)
1:4 — 1 : 4 cannot come from these formulas. With the same r and h, πr²h cancels completely and leaves 1⁄3 : 1.
(d)
1:6 — 1 : 6 is the ratio for a cone half the cylinder's height, (1⁄3)πr²(h⁄2) : πr²h. Here the heights are equal, so it stays 1 : 3.

Concept

Both solids stand on the same base area, πr². A cylinder carries that area straight up through height h. A cone tapers from it to a point, and the taper costs it two-thirds of the volume: V = (1⁄3)πr²h.

So when r and h match, the ratio is fixed at 1 : 3 whatever the actual sizes. Put the other way, three such cones of water fill the cylinder.

Key facts

Volume of a cone = (1⁄3)πr²h.
Volume of a cylinder = πr²h.
With equal radius and height, cone : cylinder = 1 : 3.

Study next

Cone, hemisphere and cylinder with height equal to the radiusPercentage change in a cone's volume when r and h changeCurved surface area of a cone from its slant height

Common traps

Inverting the ratio to 3 : 1, which answers cylinder to cone
Looking for sizes the question never gives, when πr²h cancels and the ratio needs none

26 Sep 2024, 16:00, Quant Q.3 uses the same (1⁄3)πr²h directly: a cone of radius 3.5 cm and height 18 cm, keyed 231 cm³.

17 Sep 2025, 16:00, Quant Q.13 raises a cone's radius by 20% and cuts its height by 10%, keyed a 29.6% increase.

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