SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 23 of 99

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.

The radius of the base of a right circular cone is 9 cm and its slant height is 49 cm. Find the curved surface area of the cone.

Answer

Why

Correct — C. Curved surface area of a right circular cone = πrl, where l is the slant height, not the vertical height.

r = 9 cm and l = 49 cm
CSA = (22⁄7) × 9 × 49
49 ÷ 7 = 7, so the fraction clears exactly
= 22 × 9 × 7

22 × 63 = 1386 cm², which is what option (c) prints → option (c)

The vertical height never enters the formula, and the question does not supply it.

Why the others are wrong

(a)
Option (a) prints 1490 cm². The product 22 × 9 × 7 must be divisible by 9, and 1 + 4 + 9 + 0 = 14 is not, so 1490 cannot be πrl with r = 9.
(b)
Option (b) prints 1265 cm², which would need π ≈ 2.87. Even taking π = 3.14 gives 3.14 × 441 = 1384.7 cm², about 1385.
(d)
Option (d) prints 1262 cm², a near-twin of option (b), and needs π ≈ 2.86. The arithmetic here is exact because 49 is a multiple of 7, so nothing rounds.

Concept

A cone carries three surface quantities and they are easy to confuse.

CSA = πrl covers only the sloping side. TSA = πr(l + r) adds the flat base circle. Volume = ⅓πr²h uses the vertical height, not the slant.

Slant height, radius and vertical height are tied by l² = r² + h². This question hands you r and l directly, so the height plays no part at all.

Watch the numbers before reaching for a calculator: a slant height of 49 against π = 22⁄7 cancels exactly, leaving 22 × 9 × 7 in whole numbers.

The four options are supplied as images, so the numerals have to be read off the pictures. Option (c) reads 1386 cm².

Key facts

Curved surface area of a right circular cone is πrl, with l the slant height.
Total surface area is πr(l + r), which here would be (22⁄7) × 9 × 58 ≈ 1640.6 cm².
With r = 9 and l = 49, CSA = (22⁄7) × 9 × 49 = 22 × 63 = 1386 cm².
Slant height, radius and height satisfy l² = r² + h², so h = √(2401 − 81) ≈ 48.2 cm for this cone.

Study next

Curved against total surface area for cones, cylinders and hemispheresUsing l² = r² + h² to move between slant height and vertical heightVolume of a cone, including cones formed by rotating a right triangle

Common traps

Adding the base circle and answering the total surface area of about 1640.6 cm².
Feeding the slant height into the volume formula in place of the vertical height.
Computing h first, which costs time and is never asked for.

Cone formulas are set on the volume side too. Volume from radius and height is asked at 26 Sep 2024, 16:00, Quant Q.3, and at 10 Sep 2024, 12:30, Quant Q.12 a 3-4-5 right triangle is rotated about its 3 cm side and the volume of the cone it sweeps out is wanted.

Related PYQs

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