GATE BT 2021 | GA | Question: 6

Question

We have $2$ rectangular sheets of paper, $M$ and $N$, of dimensions $6$ cm $\times$ $1$ 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 _____________

• A. $\frac{\pi}{2}\\$
• B. $\frac{3}{\pi} \\$
• C. $\frac{9}{\pi} \\$
• D. $3 \pi$

Answer 1

2πr = 6
r = 3/π

Cylinder volume:

V₁ = πr²h
= π × (3/π)² × 1
= π × 9/π²
= 9/π

Now sheet N area = 6 cm²

To make largest closed cube → 6 equal squares

Each square area = 1 cm² → side = 1 cm

Cube volume:

V₂ = 1

Ratio (Cylinder : Cube):

9/π : 1 = 9/π