Question

In the figure,a rectangular tin foil of size 22cm by 16cm is wraped around to form a cylinder of height 16cm.Find the volume of the cylinder.

Answer 1

In the first step, we had to find the radius of the cylinder by comparing the circumference of the base of cylinder with the length of the given rectangle.
Rest is as shown in the image.

Answer 2

$\bold{616 \mathrm{cm}^{3}}$ is the given cylinder’s volume

Given:

The length of the given rectangular foil is 22 cm.

The Breadth of the given rectangular foil is 16 cm.

The height of the given rectangular foil is 16 cm.

To Find:

The cylinder volume by the given dimensions.

Solution:

The cylinder’s circumference is in the shape of circle. So, the formula for the circumference of cylinder base is, $2 \pi r$

As we know that, the “circumference of the cylinder base” is equal to the rectangular foil’s length.

Therefore, we can find the “radius of the cylinder”,

$\begin{array}{l}{2 \pi r=22} \\ {r=\frac{22}{2 \times \pi}}\end{array}$

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

Radius of the cylinder, $r=\frac{7}{2} \mathrm{cm}$

And also we know that, the cylinder’s height is equal to the rectangular foil’s breadth.

Volume of the cylinder formula is, $=\pi r^{2} h$

$\begin{array}{l}{=\pi \times\left(\frac{7}{2}\right)^{2} \times 16} \\ {=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 16}\end{array}$

$\begin{array}{c}{=\frac{22 \times 7 \times 16}{4}} \\ {=616 \mathrm{cm}^{3}}\end{array}$

Volume of the cylinder is $\bold{616 \mathrm{cm}^{3}}$