Question

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold?​

Answer 1

$\dag \: \underline{\sf AnsWer :}$

• We have provided an cylindrical vessel whose circumference of base is 132 cm and it's height is 25 cm. We are asked to find that how many litres of water can ithold means we have to find the volume of cylinder. So, first we need to find the radius of cylinder and then we will find the volume of cylinder. Let's solve it :

$\bigstar\:\underline{\textbf{According to the Question Now :}}$

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

$:\implies \sf 132= 2 \times \dfrac{22}{7} \times r$

$:\implies \sf 132 \times 7 = 2 \times 22 \times r$

$:\implies \sf 924= 44 \times r$

$:\implies \sf r = \dfrac{924}{44}$

$:\implies \underline{ \boxed{\sf r = 21 \: cm }}$

$\bigstar\:\underline{\textbf{Volume of the cylinder :}}$

$\dashrightarrow\:\:\sf Volume \: of \: cylinder = \pi r^2 h$

$\dashrightarrow\:\:\sf Volume \: of \: cylinder = \dfrac{22}{7}\times 21 \times 21 \times 25$

$\dashrightarrow\:\:\sf Volume \: of \: cylinder = 22\times 3 \times 21 \times 25$

$\dashrightarrow\:\: \underline{ \boxed{\sf Volume \: of \: cylinder = 34650 \: {cm}^{3}}}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Volume \: of \: cylinder = 34.65 \:Litres }}$

Answer 2

$\bf{\underline{\underline{Answer:}}}$

$\bf {34.65\: litres\: of\: water\: it \:can\: hold}$

$\bold{\underline {Given:}}$

Height (h) =25 cm

Circumference of the base =132 cm

$\bold{\underline {To\:Find:}}$

Number of litres of water it can hold =?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Let $r$ be the radius of the base and $h$ be the height of the cylindrical vessel.

As above given,

Height (h) = 25 cm

Also, circumference of the base = 132 cm.

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

$\therefore\:\:\:\:\:\:\:\tt2\pi r = 132\: cm\\ \\ \tt\implies 2 \times \pi \times r = 132 \:cm \\ \\ \tt\implies r = \dfrac{132}{2 \pi}\:cm\\ \\ \tt\implies r =\dfrac{132}{{2 \times\dfrac{22}{7}}}\:cm\\ \\ \tt\implies r=\dfrac{\cancel {132}^{\:\cancel{66}\:^3}\times7}{\cancel2 \times\cancel {22}} \:cm\\ \\ \tt\implies r = 3\times 7\:cm \\ \\ \tt\implies r = 21\: cm$

Now, amount (volume of water = volume of the cylindrical vessel = $\pi r^2h$

$\bigstar{\boxed{\bf{\tt Volume\: of\: Cylinder = \pi r^2 h}}}$

$=\tt\dfrac{22}{7} × 21 × 21 × 25\: cm^3\\ \\ = \tt22 ×3×21×25 \:cm^3 \\ \\ = \tt34650\: cm^3$

Number of litres water can it hold =

$\bigstar{\boxed{\bf{\tt1\:litre = 1000 cm^3}}}$

$\therefore\:\:\:= \tt\dfrac{34650}{1000}l\\ \\\:\:\:\:\:\:=\tt\dfrac{34.650}{1 \cancel{000}}l \\ \\ \:\:\:\:\:\:{=\tt34.65\: litres}$

Thus, 34.65 litres of water it can hold.