SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · Quantitative Aptitude · Question 22 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.

If the height of a right prism is increased by 50% and base area remains the same, what is the percentage increase in volume?

(a)25%
(b)50%
(c)75%
(d)100%

Answer

Why

Correct — B. Volume of a right prism = base area × height, and here only the height changes.

Old volume: V = A × h
Raise the height by 50%: h becomes 1.5h
New volume: A × 1.5h = 1.5V
Increase: 1.5V − V = 0.5V = 50% → option (b)

Why the others are wrong

(a)
25% — 25% is half the height change. With the base fixed, volume is directly proportional to height, so it rises by the full 50%.
(c)
75% — 75% would need the height multiplied by 1.75. With the base unchanged, the volume factor equals the height factor, 1.5.
(d)
100% — 100% means the volume doubles, which needs the height doubled. A 50% rise makes the volume 1.5 times, not 2 times.

Concept

For any right prism, volume = area of the base × height, whatever shape the base has. With the base fixed, volume is directly proportional to height.

So a percentage change in height passes straight through to volume. It is a change in a squared length, such as a cylinder's radius, that gets amplified: a 50% rise in radius multiplies volume by 1.5² = 2.25.

Key facts

Volume of a right prism = base area × height.
With the base fixed, a k% rise in height gives a k% rise in volume.
A length that is squared in a volume formula scales the volume by the square of its factor.

Study next

Percentage change in cylinder or cone volume when radius and height both changeLateral surface area of a prism = perimeter of the base × heightVolume change when every edge of a cuboid is scaled by the same factor

Common traps

Squaring the factor out of habit (1.5² = 2.25, a 125% rise) when only the height changes.
Reading a 50% increase as a factor of 0.5 instead of 1.5.

12 Sep 2025, 16:00, Quant Q.21 also changes only the height: a triangular prism with base 25 cm² and height 10 cm has its height raised by 20%, keyed 300 cm³.

17 Sep 2025, 16:00, Quant Q.13 shows the squared case: a cone's radius rises 20% and its height falls 10%, keyed a 29.6% increase.

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.