SSC CGL 2025 Tier-I · 20 September 2025, Shift 1 · 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.

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 prism with a square base of side length 5 cm is constructed in layers. Its height follows an arithmetic progression, increasing from 4 cm in the first layer to 16 cm in the fourth layer. What is the total volume of the prism?

(a)800 cm³
(b)950 cm³
(c)1000 cm³
(d)1200 cm³

Answer

Why

Correct — C.
Layer heights form an AP: first = 4 cm, fourth = 16 cm
Common difference: (16 − 4) ÷ 3 = 4 cm
Heights: 4, 8, 12, 16 cm

Total height = 4 + 8 + 12 + 16 = 40 cm
Base area = 5 × 5 = 25 cm²
Volume = 25 × 40 = 1000 cm³ → option (c)

Why the others are wrong

(a)
800 cm³ — 800 cm³ ÷ 25 cm² is a total height of 32 cm. The four layers 4 + 8 + 12 + 16 add to 40 cm, not 32.
(b)
950 cm³ — 950 cm³ ÷ 25 is 38 cm of height. Four AP layers running from 4 to 16 cm always sum to 4⁄2 × (4 + 16) = 40 cm, never 38.
(d)
1200 cm³ — 1200 cm³ needs a total height of 1200 ÷ 25 = 48 cm. The layers give 40 cm, so this overshoots by 8 cm × 25 cm² = 200 cm³.

Concept

A prism's volume is base area × height. Stacking layers with the same square base just adds their heights, so the whole solid is one prism of height 4 + 8 + 12 + 16.

The sum of an AP needs only the count and the two ends: Sₙ = n⁄2 × (first + last) = 4⁄2 × (4 + 16) = 40. You do not even need the common difference.

The key reads 'its height follows an arithmetic progression' as four layer heights of 4, 8, 12 and 16 cm. Read as a running total, the prism would be only 16 cm tall and 400 cm³, which is not among the choices.

Key facts

Volume of a prism = base area × height
Sum of an AP = n⁄2 × (first term + last term)
nth term of an AP = a + (n − 1)d, so 16 = 4 + 3d gives d = 4

Study next

Volume of a prism with a hexagonal or triangular baseSum of the first n terms of an AP from a and dChange in a prism's volume when its height changes by a percentage

Common traps

Dividing (16 − 4) by 4 instead of 3 — four layers have three gaps
Multiplying the base area by the tallest layer alone, 16 cm, which gives 400 cm³

18 Sep 2025, 09:00, Quant Q.15 builds the same kind of stack on a regular hexagonal base of side 10 cm: section heights 5, 7, 9 and 11 cm total 32 cm, and 150√3 × 32 gives the 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.