Question

Find the volume of largest cylinder formed when a rectangular piece of paper 22cm by 15cm is rolled along its longer side. Solve and explain.

Answer 1

See, if we rolled along the longer side, that is 22 cm, then that will become the circumference of the circular ends.

2πr = 22
⇒r = 3.5 cm
and height = 15 cm

volume of the cylinder = πr²h
                                    =(22/7)×(3.5)²×15
                                    =577.5 cm³

Answer 2

The volume of the cylinder formed will be 577.5 cm³.

Given,

A rectangular paper is rolled along its length to form a cylinder.

Paper dimensions: $22 cm \times 15cm$

To find,

The volume of the cylinder formed.

Solution,

Here, the given rectangular piece of the paper has dimensions as follows,

$l=22cm,$

$b=15cm.$

Now, it can be observed that when the rectangular piece of paper is rolled along the length (longer side) to form a cylinder, the length will become the circumference of the circular ends of the cylinder, and the width of the paper will be the height of the cylinder.

Thus, the height of the cylinder, h = 15 cm, and the radius of the ends can be determined as follows.

So, if r is the radius of the circular ends, then,

$2\pi r=l$

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

Rearranging and simplifying, we get,

$r=\frac{7}{2}$

⇒ r = 3.5 cm

Now, we know that the volume of a cylinder with radius r, and height h, is given by,

$V= \pi r^2h$

$\implies V= \frac{22}{7} \times (3.5)^2 \times (15)$

Simplifying,

$V= 22\times (0.5) \times (3.5) \times (15)$

⇒ V = 577.5 cm³.

Therefore, the volume of the cylinder formed will be 577.5 cm³.