A rectangular sheet of paper 88 cm × 10 cm is folded without overlapping to make a cylinder of height 10 cm. What is the capacity (in litres) of the cylinder ? (Take $\pi =\frac{22}{7}$)

The correct option is 6.16.

Step 1: Understand the conversion of the sheet into a cylinder
When a rectangular sheet of paper is folded along its length to form a cylinder of height 10 cm, the length of the rectangular sheet becomes the perimeter (circumference) of the base of the cylinder, and the width of the sheet becomes the height of the cylinder.

Given parameters:
Length of the rectangular sheet = 88 cm
Width of the rectangular sheet (height of cylinder, h) = 10 cm

Step 2: Find the radius of the base of the cylinder
Let r be the radius of the circular base of the cylinder.
The circumference of the base of the cylinder is given by the formula:

$2\pi r=88$

Substitute $\pi =\frac{22}{7}$ into the equation:

$2\times \frac{22}{7}\times r=88$

$\frac{44}{7}\times r=88$

$r=\frac{88\times 7}{44}$

$r=2\times 7=14\text{cm}$

Step 3: Calculate the volume of the cylinder
The formula for the volume (V) of a cylinder is:

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

Substitute the values of r = 14 cm and h = 10 cm:

$V=\frac{22}{7}\times {\left(14\right)}^2\times 10$

$V=\frac{22}{7}\times 196\times 10$

$V=22\times 28\times 10$

$V=6160{\text{cm}}^3$

Step 4: Convert volume to capacity in litres
We know that 1 litre = 1000 cm³. Therefore, to convert cm³ to litres, divide the volume by 1000:

$\text{Capacity}=\frac{6160}{1000}=6.16\text{litres}$

Thus, the capacity of the cylinder is 6.16 litres.