Question

A rectangular aluminium is 44cm long and 30cm wide. A cylinder is made by rolling it. find its volume.​

Answer 1

$\huge\bold\red{Answer}$

According to the question

• Given

Length of a rectangular aluminium foil = 44 cm

Breadth of a rectangular aluminium foil = 30 cm

A cylinder is made by rolling the rectangular aluminium foil.

• To find

Volume of the cylinder

• Solution

As a cylinder is made by using the rectangular aluminium foil, length and the breadth remains the same.

Using formula,

Circumference = 2πr

where,

r = radius

Take π = 22/7

⟶ 44 = 2πr

⟶ 44 = 2 × 22/7 × r

⟶ 44 = 44/7 × r

⟶ r = 7

Radius = 7 cm

Using formula,

Volume of cylinder = πr²h

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Take π = 22/7

r = radius

h = height

Substituting their values,

=22/7 × 7 × 7 × 20

=3080 cm³

Therefore,

The final answer is

Volume of the cylinder = 3080 cm³

Answer 2

Analysis→

Here the question conveys that a rectangular aluminium whose length is 44cm and breadth is 30cm is rolled into a cylinder. Therefore, the length of rectangle will be equal to that height of the cylinder, the breadth of rectangle will be equal to the cylinder's circumference. And we've to find the volume of the cylinder. And we know that :

${\dashrightarrow{\bf{Circumference\:of\:circle=2\pi r}}}$

${\dashrightarrow{\bf{Volume\:of\:cylinder=\pi r^2h}}}$

Given→

• Height of cylinder=44cm
• Circumference of circle=30cm
• Assuming pi( $\pi$ )= $\rm\dfrac{22}{7}$

To Find→

Volume of the cylinder.

Answer→

$\maltese$ First let's find the radius of the cylinder form the given circumference.

$\implies\rm{Circumference=2\pi r}$

$\implies\rm{30cm=2\times{22}{7}\times r}$

$\implies\rm{30cm\times7=44\times r}$

$\implies\rm{r=\dfrac{30cm\times7}{44}}$

$\implies\rm{r=\dfrac{210cm}{44}}$

$\implies\rm{r=\dfrac{\cancel{210cm}}{\cancel{44}}}$

$\implies\rm{r=4.772cm}$

$\implies\rm{r≈4.77cm}$

${\boxed{\boxed{\implies{\bf{r=4.77cm\checkmark}}}}}$

_________________________

$\maltese$ Now we've found the radius, so let's find the volume ahead »

$\implies\rm{Volume=\pi r^2h}$

${\implies{\rm{Volume=\dfrac{22}{7}\times\big(4.77cm\big)^2\times44cm}}}$

${\implies{\rm{Volume=\dfrac{22}{7}\times22.7529cm^2\times44cm}}}$

${\implies{\rm{Volume=\dfrac{22\times22.7529cm^2\times44cm}{7}}}}$

${\implies{\rm{Volume=\dfrac{500.5628cm^2\times44cm}{7}}}}$

${\implies{\rm{Volume=\dfrac{22024.8072cm^3}{7}}}}$

$\implies\rm{Volume=\dfrac{\cancel{22024.8072cm^3}}{\cancel{7}}}$

$\implies\rm{Volume=3146.401cm^3}$

$\implies\rm{Volume≈3146.4cm^3}$

${\boxed{\boxed{\bf{\therefore Volume\:of\:cylinder=3146.4cm^3\checkmark}}}}$

☞ Hence the volume of the cylinder is 3146.4cm³ which is the required answer.

HOPE IT HELPS.