Question

15. A rectangular piece of paper 44 cm x 5 cm is folded without overlapping to make a cylinder of height 5 cm . Find the volume of the cylinder . ( Take
$\pi$
= 22/7 )​

Answer 1

Given :

A rectangular piece of paper 44 cm x 5 cm is folded without overlapping to make a cylinder of height 5 cm .

To Find :

Find the volume of the cylinder.

Solution :

Let radius of circle = r

Let height of circle = 5 cm

Circumference of base of circle

2πr = 44 cm

2 × 22/7 × r = 44

r = 7 cm.

Now,

Volume of cylinder = πr²h

= 22/7 × (7)² × 5

= 22/7 × 49 × 5

= 770 cm²

Therefore,

Volume of cylinder is 770 cm²

Answer 2

Given :

• A rectangular piece of paper of dimensions 44cm × 5cm is folded without overlapping to make a cylinder of height 5cm

To find :

• The volume of the so-formed cylinder

Solution :

• To find the volume, first we need to find the radius of the cylinder

$\sf Circumference \: of \: the \: base \: of \: cylinder = 2 \pi r$

$\sf \implies {44cm = 2 \pi r}$

$\sf \implies {44 = 2 \times {\dfrac{22}{7}} \times r}$

$\sf \implies {2 \times {\dfrac{22}{7}} \times r = 44}$

$\sf \implies{ {\dfrac{22}{7}} \times r = {\dfrac{44}{2}}}$

$\sf \implies{ {\dfrac{22}{7}} \times r = 22}$

$\sf \implies{r = 22 \div {\dfrac{22}{7}}}$

$\sf \implies {r = \cancel{22} \times {\dfrac{7}{ \cancel{22}}}}$

$~~~~~~\sf \therefore {\blue{ \underline{ \boxed{ \sf{ \pmb{ r = 7cm}}}}}}$

• $\sf{Volume~of~a~cylinder=\pi r^{2}h}$
• Height = 5cm
• Radius = 7cm

$\sf \implies \frac{22}{7} \times (7) ^{2} \times 5 \: \: \: \: \: \\ \sf \implies \frac{22}{ \cancel{ \: 7 \: }} \times \cancel{ \: 7 \: } \times 7 \times 5 \\ \sf \implies 22 \times 7 \times 5 \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies 22 \times 35 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf \implies \blue{ \underline{ \boxed{ \sf{ \pmb{770 \: {cm}^{3} }}}}} \: \: \: \: \: \: \: \: \: \: \: \: \:$

Required answer :

• Volume of the cylinder = $\sf\pmb{770~cm^{3}}$