Question

A rectangular piece of paper 22cm long and 12cm breadth is rolled along its length to form a cylinder. Find the volume of the cylinder so formed​

Answer 1

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\sf{\orange{Given\::}}}}}$

A rectangular piece of paper 22cm long and 12cm breadth is rolled along its length to form a cylinder.

$\bf{\Large{\underline{\sf{\red{To\:find\::}}}}}$

The volume of the cylinder so formed.

$\bf{\Large{\underline{\sf{\blue{Explanation\::}}}}}$

When the rectangular piece is rolled along its length, then the length of the piece is forms the circumference of the base and the breadth of the piece becomes height of the cylinder.

We know that formula of the volume of cylinder: πr²h   [cubic units]

• Let the base radius of cylinder be r cm
• Let the height of cylinder be h cm

∴Circumference = 22cm

→ Circumference = 2πr

→ $\bf{\cancel{22}=\cancel{2}*\frac{22}{7} *r}$

→ $\bf{\cancel{11}=\frac{\cancel{22}}{7} *r}$

→ $\bf{r = \frac{7}{2} cm}$

We have height of the cylinder,[h] = 12cm

Now,

→ Volume = $\bf{\frac{22}{7} r^{2} h}$

→ Volume = $\bf{(\frac{\cancel{22}}{\cancel{7}} *\frac{\cancel{7}}{\cancel{2}} *\frac{7}{2} *12)cm^{3}}$

→ Volume = $\bf{(11*\frac{7}{\cancel{2}} *\cancel{12})cm^{3} }$

→ Volume = (11 × 7 × 6)cm³

→ Volume = 462cm³

Thus,

The volume of the cylinder formed is 462cm³.

Answer 2

Answer:

$\bold\red{Volume=461.82{cm}^{3}}$

$\huge\underline\mathfrak{Solution\::}$

★Given:-

Length of rectangular paper = 22 cm

And Breadth = 12 cm.

_______________________

Circumference of cylinder= 22 cm

=> 22 = 2πr

=> 22 = 2 × 3.1416 × r

=>22 = 6.2832r

=> r = 22/6.2832

=> r = 3.5 cm

__________________________

Now,

Height of cylinder (h) = 12 cm

Volume of cylinder = πr^2h

=> Volume = 3.1416 × (3.5)^2×12cm^3

=> Volume = 461.82 cm^3

Hope it helps you ♥ ♥ ♥