SSC CGL 2025 Tier-I · 22 September 2025, Shift 1 · Quantitative Aptitude · Question 15 of 98

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.

We doubt SSC's key on this question.

Option (c), (3√3)⁄2 : 1, is the same ratio as the keyed 3√3 : 2 with both terms halved, so two options are equal in value; this card follows SSC's key, (b).

The answer below is still the option SSC's key marks, and we solve to that option.

Two right prisms have the same height of 10 cm. One has a regular hexagonal base with side 6 cm, and the other has a square base with side 6 cm. What is the ratio of their volumes?

(a)√3 : 1
(b)3√3 : 2
(c)(3√3)⁄2 : 1
(d)3 : 2√3

Answer

Why

Correct — B. Both prisms are 10 cm tall, so their volumes are in the ratio of their base areas.

Hexagon = 6 equilateral triangles: 6 × (√3⁄4) × 6² = 54√3 cm²
Square = 6² = 36 cm²
Ratio of volumes = 54√3 × 10 : 36 × 10 = 54√3 : 36

Divide both terms by 18: 3√3 : 2 → option (b)

Why the others are wrong

(a)
√3 : 1 — √3 : 1 counts four triangles, not six. 4 × (√3⁄4) × 36 = 36√3, and 36√3 : 36 = √3 : 1. A regular hexagon splits into six.
(c)
(3√3)⁄2 : 1 — Equal in value to (b): multiply both terms of (3√3)⁄2 : 1 by 2 and it becomes 3√3 : 2. The key marks (b), the form with no fraction inside a term.
(d)
3 : 2√3 — 3 : 2√3 is below 1 (it equals √3 : 2 ≈ 0.87), which would make the hexagonal prism the smaller. Its base, 54√3 ≈ 93.5 cm², is far larger than 36 cm².

Concept

Volume of a right prism = base area × height. With equal heights, the height cancels and only the base areas matter.

A regular hexagon of side s splits into six equilateral triangles of side s, so its area is 6 × (√3⁄4)s² = (3√3⁄2)s².

Both bases have side 6, so s² cancels as well: the ratio is (3√3⁄2) : 1, the same as 3√3 : 2 ≈ 2.6 : 1.

Options (b) and (c) are equal in value: (3√3)⁄2 : 1 is 3√3 : 2 with both terms halved. The key marks (b). If you chose (c), your working was right and only the written form differs.

Key facts

Area of a regular hexagon of side s = (3√3⁄2)s², six equilateral triangles of (√3⁄4)s² each.
Volume of a right prism = base area × height.
Prisms of equal height have volumes in the ratio of their base areas.
A ratio keeps its value when both terms are multiplied or divided by the same non-zero number.

Study next

Area of a regular hexagon inscribed in a circle, where side = radiusVolume and lateral surface area of triangular and hexagonal prismsSimplifying ratios that contain surds

Common traps

Taking one triangle, (√3⁄4)s², as the hexagon's area: that gives 9√3 : 36 = √3 : 4.
Treating (b) and (c) as different values: they are the same ratio written two ways.

The six-triangle hexagon area also decides 21 Sep 2025, 16:00, Quant Q.9, a regular hexagon inscribed in a circle of radius 14 cm: the side equals the radius, so the area is (3√3⁄2) × 14² ≈ 509.2 cm².

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 99 SSC CGL questions on it, every solved shift.