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GATE 2021 CS – Question 6

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

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges of the sheet together. Sheet N is cut into equal square patches and assembled to form the largest possible closed cube. Assuming the ends of the cylinder are closed, the ratio of the volume of the cylinder to that of the cube is ______

  1. $\frac{\pi}{2}$
  2. $\frac{3}{\pi}$
  3. $\frac{9}{\pi}$
  4. $3\pi$

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Show answer and explanation

Correct answer: (C) $\frac{9}{\pi}$

Explanation

Cylinder: circumference 6 so r=3/π, h=1, V=πr²h=9/π. Cube: six 1x1 squares give side 1, V=1. Ratio = 9/π.