SSC CGL 2024 Tier-I · 26 September 2024, Shift 3 · Quantitative Aptitude · Question 3 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

Find the volume of a cone having base radius 3.5 cm and height 18 cm.

(a)221 cm
(b)241 cm
(c)201 cm
(d)231 cm

Answer

Why

Correct — D. Volume of a cone = (1⁄3)πr²h.

r = 3.5 cm, so r² = 12.25
With π = 22⁄7: (22⁄7) × 12.25 = 38.5
38.5 × 18 = 693
693 ⁄ 3 = 231

The volume is 231 → option (d).

Why the others are wrong

(a)
221 cm — 221 is 231 with the tens digit knocked down by one. The 7 in 22⁄7 cancels against r = 3.5, so this arithmetic ends on an exact integer, and that integer is 231.
(b)
241 cm — 241 sits 10 above the true figure. Do the division by 3 last and check it: 693 ⁄ 3 = 231, whereas 241 would need a product of 723.
(c)
201 cm — 201 is close to the curved surface area, πrl ≈ 201.7 cm², using slant height l = √(3.5² + 18²) ≈ 18.34 cm. It is a surface computed where a volume was asked.

Concept

A cone holds exactly one third of the cylinder built on the same base and height: V = (1⁄3)πr²h.

The radius is squared and the height is not, so doubling the radius multiplies the volume by four while doubling the height only doubles it.

When the radius is a multiple of 3.5 or 7, use π = 22⁄7 and cancel early: (22⁄7) × 3.5 = 11, so V = (1⁄3) × 11 × 3.5 × 18 = 11 × 3.5 × 6 = 231.

The options are printed as "231 cm" rather than 231 cm³. Volume is measured in cubic centimetres — the missing exponent is a typesetting slip in the question and not a hint that a length is wanted.

Nothing else about the item is ambiguous: base radius and perpendicular height are both given, so the volume formula applies directly.

Key facts

Volume of a cone = (1⁄3)πr²h, one third of the cylinder on the same base and height.
With r = 3.5 cm and h = 18 cm the volume is 231 cm³.
π = 22⁄7 is the intended value whenever the radius is a multiple of 7 or 3.5, because the 7 cancels.

Study next

Curved surface area πrl and total surface area πr(l + r) of a coneRecovering slant height from l = √(r² + h²) before any surface formulaCones generated by rotating a right triangle about one of its legs

Common traps

Dropping the 1⁄3 and reporting 693, which is the cylinder's volume.
Computing curved surface area when the question asks for volume.
Squaring 3.5 as 12.5 instead of 12.25.

Mensuration is asked bare here, with numbers chosen so that π = 22⁄7 cancels cleanly.

The surface-area side of the same solid appears 18 Sep 2024, 12:30, Quant Q.23 (radius 9 cm, slant height 49 cm), and a rotated 3-4-5 triangle becomes a cone at 10 Sep 2024, 12:30, Quant Q.12.

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