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GATE 2024 AG – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

A 54 cm×4 cm paper is rolled by joining its two longer edges. A cube has surface area equal to the paper area. Find cylinder-volume/cube-volume ratio.

  1. $1/\pi$
  2. $2/\pi$
  3. $3/\pi$
  4. $4/\pi$

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Correct answer: (A) $1/\pi$

Explanation

Joining the longer edges makes tube height 54 cm and circumference4 cm, so radius2/π. Cylinder volume is $\pi(2/\pi)^2(54)=216/\pi$ cm³. Paper area 216 cm² equals 6a²,so cube edgea=6 cm and volume 216 cm³. Their ratio is **1/π,A**.

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