SSC CGL 2025 Tier-I · 14 September 2025, Shift 2 · Quantitative Aptitude · Question 24 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 cylinder (r = 4 cm, h = 10 cm) is bored through by a hole (r = 2 cm, full height). What percentage of original volume is removed?

(a)25%
(b)50%
(c)75%
(d)37.5%

Answer

Why

Correct — A. The hole is a cylinder of the same height, so compare the two volumes directly.

Original: π × 4² × 10 = 160π cm³
Hole: π × 2² × 10 = 40π cm³
Divide: 40π ÷ 160π = 1⁄4 = 25% → option (a)

Why the others are wrong

(b)
50% — 50% is the ratio of the radii, 2 ÷ 4. Volume depends on radius squared, so the hole holds one quarter of the volume, not half.
(c)
75% — 75% is the share that stays: 120π of 160π cm³. The question asks for the share removed, which is 40π.
(d)
37.5% — 37.5% = 3⁄8 would need a hole with r² = 6, a radius of about 2.45 cm. A 2 cm hole gives r² = 4 against 16.

Concept

Volume of a cylinder is πr²h. When the hole runs the full height, both solids share h, so the fraction removed is (hole radius ÷ outer radius)².

That square is why halving the radius removes a quarter of the volume, not a half. The 10 cm height does not affect the percentage.

Key facts

Volume of a cylinder = πr²h.
Volume of a hollow cylinder = πh(R² − r²).
Here 160π − 40π = 120π cm³ remains, 75% of the original.

Study next

Volume of metal in a hollow pipe, πh(R² − r²)Total surface area of a bored cylinder, which gains an inner curved surfacePercentage change in cylinder volume when the radius changes by a given percent

Common traps

Comparing the radii (2 : 4) instead of their squares (4 : 16).
Answering with what remains (75%) when the question asks what is removed.

17 Sep 2025, 16:00, Quant Q.13 also turns on radius entering volume as a square: a cone's radius rises 20% while 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.