SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · Quantitative Aptitude · Question 13 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 cone is sliced into two sections by a plane that is parallel to its base, with the upper section representing 1⁄8 of the overall volume. What is the ratio of the heights of the smaller cone to the original cone?

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

Answer

Why

Correct — A. A cut parallel to the base leaves a small cone on top that is similar to the original. The upper section is that small cone.

For similar cones, volume ratio = (height ratio)³
Set up: (h⁄H)³ = 1⁄8
Cube root: h⁄H = ∛(1⁄8) = 1⁄2

Smaller cone : original cone = 1 : 2 → option (a)

Why the others are wrong

(b)
1 : 7 — 1 : 7 is the ratio of the two pieces' volumes: the top cone is 1⁄8 of the whole and the frustum below is 7⁄8. The question asks for heights.
(c)
5 : 1 — 5 : 1 makes the smaller cone five times as tall as the original. The top piece is part of the original, so its height ratio must be below 1.
(d)
6 : 1 — 6 : 1 has the smaller cone six times the original's height, which is impossible for a piece cut from it. The ratio must be less than 1.

Concept

A plane parallel to the base cuts a cone into a smaller cone on top and a frustum below. The small cone is similar to the original: its radius and height shrink by the same factor k.

Similar solids scale by powers of k: lengths by k, areas by k², volumes by k³.

So a volume fraction of 1⁄8 means k³ = 1⁄8 and k = 1⁄2. The cut is halfway up the cone's height.

Key facts

A cut parallel to the base of a cone produces a smaller cone similar to the original.
For similar solids, the volume ratio is the cube of the height ratio.
A top cone of half the height holds 1⁄8 of the volume, and the frustum below holds 7⁄8.

Study next

Volume of a frustum of a coneWhere to cut a cone so that the two parts have equal volume (h⁄H = 1⁄∛2)Ratio of curved surface areas of similar cones (square of the scale factor)

Common traps

Answering 1 : 7, the volume ratio of top cone to frustum, when the question asks for heights.
Taking the square root of 1⁄8 instead of the cube root.

19 Sep 2025, 09:00, Quant Q.13 runs it forward: a conical bucket is cut at one-third of its height from the top, so the top cone is (1⁄3)³ = 1⁄27 of the volume and the parts are keyed 1 : 26.

The same cube law drives 18 Sep 2025, 12:30, Quant Q.12, where a cuboid's three 10% rises give 1.1³ = 1.331.

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.