Question

a square piece of paper of side 22 cm is rolled to form a cylinder find the volume of the other

Answer 1

Circumference of the cylinder base = 22cm

2πr = 22 cm

44/7r = 22

∴ r = (22×7)/44 = 7/2 cm.

Now height is also of 22cm.

∴volume of the cylinder=πr²h

V=( 22/7)×(7/2)×(7/2)×22 cubic cm

V = 847 cubic cm.

Answer 2

The volume of the other is 847 cm³.

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Let's understand a few concepts:

A certain-shaped (square or rectangle) sheet of paper when rolled into a cylinder along one of its sides then, that side forms the length of the cylinder and the adjacent side forms the circumference of the base of the cylinder.

To calculate the volume of the cylinder we will use the following formula:

$\boxed{\bold{Volume \:of\:a\:cylinder = \pi r^2 h}}$

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Let's solve the given problem:

Here we are given a square piece of paper of side = 22 cm

After rolling the square paper into cylinder, we get

Height of the cylinder (h) = side of the square = 22 cm

and

Circumference of the base of the cylinder = Length of the side of the square paper

∴ $2\pi r = 22$

$\implies r = \frac{22}{2\pi }$

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

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

$\implies r = 3.5 \:cm$ ← the radius of the cylinder

Therefore,

The volume of the cylinder is,

= $\pi r^2 h$

= $\frac{22}{7} \times 3.5^2 \times 22$

= $\frac{22}{7} \times 12.25 \times 22$

= $\bold{847\:cm^3}$

Thus, the volume of the other is 847 cm³.

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