Question

We have 2 rectangular sheets of paper, M and N, of dimensions $6cm\times 1cm$ 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.
  $\frac{9}{\pi }$
• B.
  $3\pi$
• C.
  $\frac{\pi }{2}$
• D.
  $\frac{3}{\pi }$

Answer 1

The correct option is A

$\frac{9}{\pi }$


$Volumeofcylinder=\pi r^{2}h$

$\text{Now,}2\pi r=6\left(\text{figure A}\right)$

$r=\frac{3}{\pi }$

$\text{Volume of cylinder}=\pi \times \frac{3}{\pi }\times \frac{3}{\pi }\times 1=\frac{9}{\pi }$

$\text{Volume of cube}=(1{)}^3$

$\text{Ratio}=\frac{\frac{9}{\pi }}{1}=\frac{9}{\pi }$