Question

Find the volume of cylinder which is made by rolling a rectangular sheet of size 44 cm × 33 cm along its breadth.

Answer 1

Answer :

• Volume of cylinder is 3811.5cm³

Given :

• A cylinder which is made by rolling a rectangular sheet of size 44cm × 33cm along its breadth

To find :

• The volume of cylinder

Solution :

Given that ,

• Rectangular sheet of size is 44cm × 33cm Then,

As we know that,

• Area of rectangle sheet = length × breadth

》 44 × 33

》 1452cm²

Hence , Area of rectangular sheet is 1452cm²

As we know that,

• Curved surface area of cylinder = 2πrh

》2 × 22/7 × r × 44 = 1452

》 2 × 22 × 44 / 7 × r = 1452

》 r = 1452 × 7/ 2 × 22 × 44

》r = 21/4

Hence , Radius is 21/4

Now we have to find the volume of cylinder

As we know that,

• Volume of cylinder = πr²h

》22/7 × 21/4 × 21/4 × 44

》7623/2

》 3811.5cm³

Hence , Volume of cylinder is 3811.5cm³

Answer 2

A N S W E R :

• The volume of cylinder is = $\large\underline{\rm{3811.5~cm³}}$

Given :-

• A cylinder which is made by rolling a rectangular sheet of size 44 cm × 33 cm along its breadth.

To find :-

• Find the value of cylinder ?

★ $\large\underline{\frak{As~we~know~that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Area~of~rectangle~=~length~×~breadth}}$

$\large\dashrightarrow$44 × 33

$~~~~~$$\large\dashrightarrow$${\underline{\boxed{\purple{\frak{1452~cm²}}}}}$★

$\therefore$ Hence,

• Area of the rectangle sheet is = $\large{\rm\underline{1452~cm²}}$

★ $\large\underline{\frak{As we know that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Curved ~surface~ area ~of ~cylinder ~= ~2πrh}}$

:$\implies$2 × $\large{\sf{\frac{22}{7}}}$× r × 44 = 1452

$~~~~~$:$\implies$2 × 22 × $\large{\sf{\frac{44}{7}}}$× r = 1452

$~~~~~~~~~~$:$\implies$r = 1452 × $\large{\sf{\frac{7}{2}}}$× 22 × 44

$~~~~~~~~~~~~~~~$:$\implies$r = ${\underline{\boxed{\blue{\frak {\frac{21}{4}}}}}}$★

$\large\dag$ Henceforth,

• The Radius is = $\large{\rm{\frac{21}{4}}}$

V E R I F I C A T I O N :

• Find the value of cylinder

★ $\large\underline{\frak{As we know that,}}$

$\large\dag$ Formula Used :

• $\boxed{\bf{Volume ~of ~cylinder ~= ~πr²h}}$$\large\star$

:$\implies$$\large{\sf{\frac{22}{7} × \frac{21}{7} × 44}}$

$~~~~~$:$\implies$$\large{\sf{\frac{7623}{2}}}$

$~~~~~~~~~~$:$\implies$${\cancel{\dfrac{7623}{2}}}$

$~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\pink{\frak{3811.5~cm³}}}}}$★

$\large\dag$ Hence Verified !!

• The volume of the cylinder is = $\large\underline{\rm{3811.5 ~cm³}}$