SSC CGL 2024 Tier-I · 10 September 2024, Shift 3 · Quantitative Aptitude · Question 4 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 6 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.

A rectangular piece of paper is 50 cm long and 22 cm wide. If a cylinder is formed by rolling the paper along its breadth, then the volume of the cylinder is:

Answer

Why

Correct — A. Rolling along the breadth wraps the 22 cm side round into the circumference; the 50 cm length stands up as the height.

2πr = 22
r = 22 × 7 ⁄ (2 × 22) = 3.5 cm, and h = 50 cm

Volume = πr²h
= (22⁄7) × 3.5 × 3.5 × 50
= 22 × 1.75 × 50 = 1,925 cm³

The options are printed as images; option (a) is the one reading 1,925 cm³.

Why the others are wrong

(b)
Option (b) reads 2,125 cm³. That volume needs r ≈ 3.68 cm, and 2π × 3.68 ≈ 23.1 cm — wider than the 22 cm side you actually rolled.
(c)
Option (c) reads 2,025 cm³, exactly 100 above the answer. It needs r² ≈ 12.89, whereas 2πr = 22 gives r = 3.5 and r² = 12.25 exactly, with nothing left over.
(d)
Option (d) reads 1,825 cm³, the bottom rung of the same ladder. With h = 50 fixed, the cross-section must be 1,925 ⁄ 50 = 38.5 cm², which is (22⁄7) × 3.5² precisely.

Concept

Rolling a rectangle into a cylinder keeps the sheet's area as the curved surface. One side becomes the circumference, the other becomes the height.

So a 50 cm × 22 cm sheet makes two different cylinders. Rolled along the breadth, 2πr = 22 gives r = 3.5 cm with h = 50 cm, and the volume is 1,925 cm³.

Rolled the other way — 50 cm as the circumference, 22 cm as the height — the same sheet holds 4,375 cm³. No option matches that, which confirms which reading the paper intends.

The four option values are pictures, not text, and they sit 100 cm³ apart: 1,825, 1,925, 2,025 and 2,125. Read all four before computing, because a rounded radius lands you on a neighbour.

Key facts

Rolling a rectangle into a cylinder turns one side into the circumference and the other into the height.
Along the breadth here means 2πr = 22, so r = 3.5 cm and h = 50 cm.
Volume = πr²h = (22⁄7) × 12.25 × 50 = 1,925 cm³.
Rolled the other way the same sheet would hold 4,375 cm³.

Study next

Two different cylinders from one rectangular sheet, and which dimension becomes the heightCurved surface area of a cylinder read as the area of the original rectangleVolume of a cone formed by rolling a sector of a circle

Common traps

Making the 50 cm side the circumference because it is named first in the stem
Treating 22 cm as the diameter instead of the circumference
Squaring 3.5 as 12.5 rather than 12.25

The phrase naming which side is rolled is the entire question — roll the sheet along its length instead and the 50 becomes the circumference while the 22 becomes the height.

Because the options are images of numbers rather than text, budget a moment to read them before you start.

Related PYQs

No directly related past PYQ was found.