SSC CGL 2025 Tier-I · 19 September 2025, Shift 1 · 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 conical bucket is cut at one-third its height from the top. What is the ratio of the volumes of the two parts (top part to bottom part)?

(a)1 : 8
(b)1 : 26
(c)1 : 27
(d)1 : 7

Answer

Why

Correct — B.
Cutting at a fixed height means a plane parallel to the base, so the top piece is a small cone similar to the whole.
Height ratio, top cone : whole = 1 : 3
Volume ratio = the cube of that = (1⁄3)³ = 1⁄27

Bottom piece (frustum) = 1 − 1⁄27 = 26⁄27 of the whole
Top : bottom = 1⁄27 : 26⁄27 = 1 : 26 → option (b).

Why the others are wrong

(a)
1 : 8 — 1 : 8 squares the scale factor instead of cubing it: (1⁄3)² = 1⁄9, then 1 : 8. That is the ratio of curved surface areas, not volumes.
(c)
1 : 27 — 1 : 27 compares the top cone with the whole cone. The question asks top part to bottom part, so take the top away: 27 − 1 = 26.
(d)
1 : 7 — 1 : 7 is the answer for a cut at half the height: (1⁄2)³ = 1⁄8 of the volume on top, leaving 7⁄8 below.

Concept

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

A plane parallel to a cone's base cuts off a smaller, similar cone. Here k = 1⁄3, so the top cone holds 1⁄27 of the volume and the frustum below holds the remaining 26⁄27.

The key reads the cone vertex up, so the top piece is the small cone. Read vertex down, the bottom piece would be the small cone (two-thirds of the height, 8⁄27 of the volume) and the ratio 19 : 8, which no option offers.

Key facts

For similar solids with linear ratio k, volumes are in the ratio k³.
Curved surface areas of similar solids are in the ratio k².
A cut at one-third of a cone's height, measured from the vertex, leaves 1⁄27 of the volume in the small cone.
A cut at half the height leaves 1⁄8 of the volume in the small cone and 7⁄8 in the frustum.

Study next

Volume of a frustum: (1⁄3)πh(R² + Rr + r²)Cutting a cone into equal-volume pieces with planes parallel to the baseCurved surface area of a cone against that of its frustum

Common traps

Squaring the height ratio, which gives an area ratio (1 : 8)
Comparing the top piece with the whole cone (1 : 27) instead of with the frustum

18 Sep 2025, 12:30, Quant Q.13 runs the same cube law backwards: the top section is 1⁄8 of the volume, so the height ratio is ∛(1⁄8) = 1⁄2, keyed 1 : 2.

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.