SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 21 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.

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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 triangular prism has base area of 25 cm². If height is increased by 20%, what is the new volume (original height was 10 cm)?

(a)250 cm³
(b)275 cm³
(c)300 cm³
(d)225 cm³

Answer

Why

Correct — C. The volume of any prism is base area × height, and the base area stays 25 cm².

Raise the height by 20%: 10 × 1.2 = 12 cm
Multiply by the base: 25 × 12 = 300 cm³ → option (c)

Check: the old volume was 25 × 10 = 250 cm³, and 250 × 1.2 = 300 cm³.

Why the others are wrong

(a)
250 cm³ — 250 cm³ is the original volume, 25 × 10. It leaves out the 20% increase in height that the question asks about.
(b)
275 cm³ — 275 cm³ = 25 × 11, which needs a height of 11 cm, a 10% increase. A 20% increase takes the height to 12 cm.
(d)
225 cm³ — 225 cm³ = 25 × 9, less than the original 250 cm³. It fits a 10% cut in height, but the question raises the height.

Concept

A prism has the same cross-section all along its length, so its volume is base area × height whatever the shape of the base.

With the base fixed, volume is directly proportional to height. A 20% increase in height gives a 20% increase in volume: 250 × 1.2 = 300 cm³.

In a triangular prism, height means the distance between the two triangular faces, not the height of the triangle. The 25 cm² base area is already the triangle's area, so the triangle's own height is never needed.

Key facts

Volume of a prism = base area × height.
With the base area unchanged, a p% change in height gives a p% change in volume.
25 cm² × 12 cm = 300 cm³.

Study next

Lateral surface area of a prism: perimeter of the base × heightPercentage change in volume when two dimensions change togetherArea of a triangular base from its three sides, by Heron's formula

Common traps

Stopping at the original volume, 25 × 10 = 250 cm³, before applying the 20% rise.
Multiplying by ½ as if the triangle's base and height were given: 25 cm² is already an area, so volume = 25 × 12 with no ½.

The same proportionality is asked directly at 14 Sep 2025, 12:30, Quant Q.22: a right prism's height rises 50% with the base unchanged, so its volume rises 50%.

At 21 Sep 2025, 16:00, Quant Q.14 it runs backwards: 1024 ÷ 16 gives a 64 cm² square base, so the side is 8 cm.

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.