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GATE 2024 MT – Question 7

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

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

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

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

Explanation

Joining the long edges makes circumference 4 cm and height 54 cm, so r=2/π and Vtube=216/π cm³.

The sheet area is 216 cm²; cube surface 6a²=216 gives a=6 cm and Vcube=216 cm³.

Thus the ratio is **1/π, A**.