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GATE 2021 CH – 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 × 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. $\pi/2$
  2. $3/\pi$
  3. $9/\pi$
  4. $3\pi$

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Correct answer: (C) $9/\pi$

Explanation

**Cylinder:** joining the short edges makes the 6 cm side the circumference and the 1 cm side the height. Therefore $2\pi r=6$, $r=3/\pi$ and $V_c=\pi r^2h=9/\pi\ \mathrm{cm^3}$.

**Cube:** the sheet provides six unit squares, giving six faces of side 1 cm. This also uses the entire available area, so a larger closed cube is impossible. Its volume is $1\ \mathrm{cm^3}$.

Hence $V_c/V_{cube}=\mathbf{9/\pi}$, **option C**.