Question

The circumference of the base of a cylendrical vessel is 132 cm and its height is 25 cm how many litres of water can it hold.(1000 cm^3= 1 litre)

Answer 1

AnswEr :

34.650 l.

$\bf{\blue{\underline{\underline{\bf{Given\::}}}}}$

The circumference of the base of a cylindrical vessel is 132 cm and it's height is 25 cm.

$\bf{\blue{\underline{\underline{\bf{To\:find\::}}}}}$

The capacity of water can it hold.

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

We have;

• Circumference of cylinder = 132 cm
• Height of cylinder = 25 cm

Then;

$\leadsto\sf{Circumference\:of\:circle\:=2\pi r}\\\\\\\leadsto\sf{132\:cm=2\times \dfrac{22}{7} \times r}\\\\\\\leadsto\sf{132\:cm=\dfrac{44}{7} \times r}\\\\\\\leadsto\sf{132\:cm\times 7=44r}\\\\\\\leadsto\sf{924\:cm=44r}\\\\\\\leadsto\sf{r=\cancel{\dfrac{924}{44}} cm}\\\\\\\leadsto\sf{\red{r=21\:cm}}$

Formula use :

$\bf{\boxed{\sf{Volume\:of\:Cylinder\:(V)=\pi r^{2} h\:\:\:\:(cubic\:unit)}}}}}$

$\mapsto\tt{Volume_{(cylinder)}=\pi r^{2} h}\\\\\\\mapsto\tt{Volume_{(cylinder)}=\bigg(\dfrac{22}{\cancel{7}} \times \cancel{21} \times 21\times 25\bigg)cm^{3} }\\\\\\\mapsto\tt{Volume_{(cylinder)}=(22\times 3\times 21\times 25)\:cm^{3} }\\\\\\\mapsto\tt{Volume_{(cylinder)}=(66\times 21\times 25)\:cm^{3} }\\\\\\\mapsto\tt{\red{Volume_{(cylinder)}=34650\:cm^{3} }}$

We know that;

→ 1 litres = 1000 cm³

→ 1 cm³ = 1/1000 litres

$\leadsto\sf{\cancel{\dfrac{34650}{1000} }\:litres}\\\\\\\leadsto\sf{34.650\:litres}$

Thus,

The capacity of water can it hold is 34.650 litres .

Answer 2

Answer:

Step-by-step explanation:

Let radius=r cm

Height=h=25cm

Circumference of the cylinder=132cm

2*pi*r=132

r=(132*7)/(2*22)

r=21cm

Capacity of the vessel=volume of the vessel

=pi*r^2*h

=22/7*21*21*25

=34650cm^3

=34650*1/1000 li

[since 1cm^3= 1/1000 li]

=34.65li

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