Question

The circumference of the Base of a cylindrical vessel is 132cm and it's height is 25cm. How many litres of water can it hold

Answer 1

Given :-

Circumference of base of cylinder (2πr) =132cm

Height of vessel = 25cm

To find :-

• The volume of Cylinder

$\bigstar{\boxed{\sf{Circumference\ of \ circle = 2 \pi r}}}$

• First find the value of r

$\longmapsto\sf 2\pi r = 132\\ \\ \sf\ \ \ take\ \ \pi =\dfrac{22}{7}\\ \\ \longmapsto\sf 2\times\dfrac{22}{7}\times r=132\\ \\ \longmapsto\sf \dfrac{44r}{7}=132\\ \\ \longmapsto\sf r=\cancel{132}\times \dfrac{7}{\cancel{44}}\\ \\ \longmapsto\sf r= 3\times 7\\ \\ \longmapsto\sf r= 21cm$

$\boxed{\sf{ radius (r)=21cm}}$

Now the volume of cylinder

$\bigstar{\boxed{\sf{ Volume \ of \ cylinder= \pi r^2h}}}$

We have

• Radius (r)=21cm

• Height (h)=25cm

$\longmapsto\sf Volume = \pi r^2 h\\ \\ \longmapsto\sf Volume = \dfrac{22}{\cancel7}\times \cancel{21}\times 21\times 25\\ \\ \longmapsto\sf Volume = 22\times 3\times 21\times 25\\ \\ \longmapsto\sf Volume = 66\times 525\\ \\ \longmapsto\sf Volume = 34650cm^3\\ \\ \sf\ \ In \ \ litre \ \ 1litre = 1000cm^3\\ \\ \longmapsto\sf 34650cm^3 =\dfrac{34650}{1000}\ litre\\ \\ \longmapsto\sf Volume = 34.6\ litre$

$\boxed{\sf{\dag\ \ vessel\ can \ hold \ 34.6\ litre \ water }}$

Answer 2

$\rule{302}{2}$

GIVEN :-

Circumference of the base of a cylinder = 132 cm

Height of the vessel = 25 cm

TO FIND :-

The capacity of the vessel (i.e. the volume of the vessel).

FORMULAE TO BE USED :-

• Circumference of a circle = 2πr

• Volume of a cylinder = πr²h

• π = 22/7

SOLUTION :-

A/q,                                       

$\sf 2\pi r = 132\\ \\ \sf\ \ \implies \sf 2\times\dfrac{22}{7}\times r=132\\ \\ \implies\sf \dfrac{44r}{7}=132\\ \\ \displaystyle{\implies\sf r=\frac{(132\times7)}{44}} \\ \\ \implies\sf r= \frac{924}{44} \\ \\ \boxed{\implies\sf r= 21\ cm}$    

Now, volume of the cylinder :-

$\implies \sf Volume = \pi r^2 h\\ \\ \implies\sf V= \dfrac{22}{\cancel7}\times \cancel{21}\times 21\times 25\\ \\ \implies\sf V = 22\times 3\times 21\times 25\\ \\ \implies\sf V= 66\times 525\\ \\ \implies\sf V= 34650\ cm^3$

→ We know, 1 litre = 1000 cm³                      

$\displaystyle{\implies \sf V=34650\ cm^3=\frac{34650}{1000}\ l }}\\\\\underline{\boxed{\boxed{\implies \sf V=34.65\ l}}}}$        

∴ Thus, the vessel can hold 34.65 litres of water in it.

$\rule{302}{2}$