SSC CGL 2025 Tier-I · 19 September 2025, Shift 2 · Quantitative Aptitude · Question 15 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.

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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 prism has an equilateral triangular base with a side length of 4 cm. Its height starts at 5 cm and increases by 1 cm for each subsequent layer, forming 5 layers in total. What is the total volume of the prism? (Use √3≈1.732)

(a)207.84 cm³
(b)242.48 cm³
(c)259.80 cm³
(d)303.10 cm³

Answer

Why

Correct — B.
Base area, equilateral triangle of side 4: (√3⁄4) × 4² = 4√3 cm²
Layer heights: 5, 6, 7, 8, 9 cm
Add them: 5 + 6 + 7 + 8 + 9 = 35 cm

Volume = base area × total height = 4√3 × 35 = 140√3 cm³
Use √3 ≈ 1.732: 140 × 1.732 = 242.48 cm³ → option (b)

Why the others are wrong

(a)
207.84 cm³ — 207.84 cm³ is 120 × 1.732, which is 4√3 × 30, a total height of 30 cm. The five layers add to 35 cm, not 30.
(c)
259.80 cm³ — 259.80 cm³ is 150 × 1.732, which is 4√3 × 37.5, a total height of 37.5 cm. Five layers rising from 5 cm by 1 cm add to 35 cm.
(d)
303.10 cm³ — 303.10 cm³ is 175 × 1.732, which is 4√3 × 43.75, a total height of 43.75 cm. That is 8.75 cm more than the 35 cm the five layers stack to.

Concept

A prism's volume is base area × height. Layers that share one base simply add, so you can add the heights first and multiply once.

The heights 5, 6, 7, 8, 9 form an arithmetic progression. Its sum is n⁄2 × (first + last) = 5⁄2 × (5 + 9) = 35.

The base is an equilateral triangle, so its area is (√3⁄4)a², not ½ × a × a.

The stem's "layers" are read as five stacked pieces on the same triangular base, with heights 5 to 9 cm. That reading gives the keyed 242.48 cm³. One prism of final height 9 cm would give about 62.35 cm³, which is not among the options.

Key facts

Volume of a prism = base area × height
An equilateral triangle of side 4 cm has area 4√3 ≈ 6.928 cm²
Sum of an arithmetic progression = n⁄2 × (first term + last term)

Study next

Layered prisms on a square or regular hexagonal baseLateral surface area of a prism: base perimeter × heightSum of the first n terms of an arithmetic progression

Common traps

Using the last layer's height, 9 cm, alone, which gives about 62.35 cm³
Taking the base as ½ × 4 × 4 = 8 cm², a right triangle's area, instead of (√3⁄4) × 4²

20 Sep 2025, 09:00, Quant Q.15 builds the same kind of prism on a 5 cm square base with heights 4, 8, 12, 16 cm, keyed 1000 cm³ (25 × 40).

18 Sep 2025, 09:00, Quant Q.15 stacks pieces of 5, 7, 9, 11 cm on a regular hexagon of side 10 cm, keyed 4800√3 cm³.

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.