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GATE CSE 2024 Session 1 Q7: Volume ratio of a rolled paper tube to a cube of equal area

Question

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

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Answer: A (official GATE 2024 final answer key)

Concept used: Joining the longer edges makes the short edge the circumference and the long edge the height.

First step: Circumference 2πr=42\pi r = 4 and height 54; the cube has 6a2=2166a^2 = 216.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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