SSC CGL 2025 Tier-I · 17 September 2025, Shift 3 · Quantitative Aptitude · Question 13 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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The radius of a cone is raised by 20%, while the height is reduced by 10%. What is the percentage change in the volume of the cone?

(a)27.4% decrease
(b)29.6% increase
(c)4.8% increase
(d)5.2% increase

Answer

Why

Correct — B.
Cone volume V = (1⁄3)πr²h, so V scales as r² × h
Radius factor: 1 + 20% = 1.2, squared = 1.44
Height factor: 1 − 10% = 0.9

Volume factor: 1.44 × 0.9 = 1.296
Change: 1.296 − 1 = 0.296 = 29.6% increase → option (b)

Why the others are wrong

(a)
27.4% decrease — A decrease is the wrong direction. Squaring the radius lifts r² by 44%, and a 10% cut in height takes back only part of that: 1.44 × 0.9 = 1.296, above 1.
(c)
4.8% increase — 4.8% would mean a volume factor of 1.048. The radius enters squared, so the factor is 1.44 × 0.9 = 1.296, a 29.6% rise.
(d)
5.2% increase — 5.2% would mean a factor of 1.052. With r² scaled by 1.44 and h by 0.9, the factor is 1.296, so the rise is 29.6%.

Concept

When a quantity is a product of powers of its dimensions, multiply the factor for each dimension raised to its power. Constants such as 1⁄3 and π cancel.

Cone volume goes as r²h, so the 20% radius rise counts twice: 1.2² = 1.44.

The same answer comes by successive percentages.
r²: 20 + 20 + (20 × 20)⁄100 = 44%
Then the height: 44 − 10 + (44 × −10)⁄100 = 34 − 4.4 = 29.6%

Key facts

Volume of a cone = (1⁄3)πr²h, so V ∝ r²h.
Successive changes of a% and b% give a net change of a + b + ab⁄100 percent.
A 20% rise in a squared quantity is a 44% rise, not 40%.

Study next

Percentage change in cylinder volume when radius and height change togetherPercentage change in a sphere's volume or surface area when its radius changesNet effect of successive percentage changes (a + b + ab⁄100)

Common traps

Treating the radius as linear: 1.2 × 0.9 = 1.08, an 8% rise that is not among the options.
Taking r² as 1.4 (20% doubled) instead of 1.2² = 1.44: 1.4 × 0.9 = 1.26, a 26% rise.

14 Sep 2025, 12:30, Quant Q.22 is the linear case: a right prism's height rises 50% with the base unchanged, and the volume rises by the keyed 50%.

12 Sep 2025, 16:00, Quant Q.21 does the same with a triangular prism (base 25 cm², height 10 cm raised 20%, keyed 300 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 51 SSC CGL questions on it, every solved shift.