Question

the circumference of the base of a cylindrical vessel is 132 cm and it's height is 25 cm . how many litres of water can it hold
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Answer 1

Given,

• The Circumference of the base of a Cylindrical vessel is 132cm.

• And The height of the Cylindrical vessel 25cm.

To Find,

• How many litres of water the Cylindrical vessel can hold?

Solution,

Let the Radius of the Cylindrical vessel be 'R'.

As given,

• The Circumference of the base of a Cylindrical vessel = 132m

Can be written as,

$:\longrightarrow 2\pi ( \text{Radius}) = 132cm \\ \\ :\longrightarrow 2 \times \frac{22}{7} \times R = 132cm \\ \\:\longrightarrow \frac{44}{7} \times R = 132cm \\ \\ :\longrightarrow R = 132cm \times \frac{7}{44} \\ \\ :\longrightarrow R = (3 \times 7)cm \\ \\:\longrightarrow R = 21cm$

Hence,

• The Radius of the Cylindrical vessel is 21 cm.

Finding the Volume of the Cylindrical vessel,

As given,

• The Height of the Cylindrical vessel is 25cm.

We found,

• The Radius of the Cylindrical vessel is 21cm.

As we know,

• $\boxed{\text{Volume}_{(\text{Cylinder})} =\pi {r}^{2} h}$

Let's Substitute the values,

$:\longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =\pi {(21cm)}^{2} (25cm)\\ \\ :\longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} = \frac{22}{7} \times 21cm \times 21cm \times 25cm \\ \\ :\longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =(22 \times 3 \times 21 \times 25) {cm}^{3} \\ \\ :\longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =34650 {cm}^{3}$

Hence,

• The Volume of the Cylindrical vessel is 34650cm³.

As we know,

• $1000 {cm}^{3} = 1l \\ \\ 1 {cm}^{3} = \frac{1}{1000} l \: \: \: \: \: \: \: ...(1)$

As we found,

• $\text{Volume}_{(\text{Cylindrical vessel})} =34650 {cm}^{3}$

Can be written as,

$: \longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =34650 \times 1{cm}^{3} \\ \\ : \longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =34650 \times \frac{1}{1000} l \: \: \: \: \: \: \: \: \: \: ... [ \text{by eq(1)}] \\ \\ : \longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} = \frac{3465}{100} l \\ \\ : \longrightarrow \text{Volume}_{(\text{Cylindrical vessel})} =34.65l$

Therefore,

• The Cylindrical vessel can hold 34.65 litres.

Required Answer,

• The Cylindrical vessel can hold 34.65 litres of water.