Question

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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? (1000 cm³ = 1 l )

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Answer 1

Given :

• The circumference of base of a cylinderical vessel is 132 cm and its height is 25 cm.

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To Find :

• How many litres of water can it hold ?

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Solution :

${\orange{❒}}$ Formula Used :

• Circumference of Circle :

$\large{\color{blue}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Circumference{\small_{(Circle)}} = 2πr }}}}}$

• Volume of Cylinder :

$\large{\color{blue}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Volume{\small_{(Cylinder)}} = πr²h }}}}}$

Where :

• ➳ Circumference = 132 cm
• ➳ π = pi = ${\sf{ \dfrac{22}{7}}}$
• ➳ h = Height = 25 m
• ➳ r = Radius = ?
• ➳ Volume = ?

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${\orange{❒}}$ Calculating the Radius :

${\longmapsto{\qquad{\sf{ Circumference{\small_{(Base )}} = 2πr }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \: \: \: 132 = 2 \times \dfrac{22}{7} \times r }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \: \: \: 132 \times 7 = 2 \times 22 \times r }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \: \: \: 924 = 44 \times r }}}} \\ \\ \ {\longmapsto{\qquad{\sf{\: \: \: \cancel\dfrac{924}{44} = r }}}} \\ \\ \ {\qquad{\sf{ Radius \: of \: the \: Base \: = {\pink{\sf{ 21 \: cm }}}}}}$

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${\orange{❒}}$ Calculating the Volume :

${\longmapsto{\qquad{\sf{ Volume{\small_{(Cylinderical \: Vessel )}} = πr²h }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume{\small_{(Cylinderical \: Vessel )}} = \dfrac{22}{\cancel7} \times \cancel{21} \times 21 \times 25 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume{\small_{(Cylinderical \: Vessel )}} = 22 \times 3 \times 21 \times 25 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Volume{\small_{(Cylinderical \: Vessel )}} = 66 \times 525 }}}} \\ \\ \ {\qquad{\sf{ Volume \: of \: the \: Cylinderical \: Vessel \: = {\green{\sf{34650 \: cm² }}}}}}$

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${\orange{❒}}$ Calculating Water it can hold :

${\dashrightarrow{\qquad{\sf{ Water{\small_{(Holded)}} = \dfrac{Volume}{1000}}}}} \: \: \: \: \bigg\lgroup{\purple{\sf{ 1000 \: cm³ = 1 \: L }}}\bigg\rgroup \\ \\ \ {\dashrightarrow{\qquad{\sf{ Water{\small_{(Holded)}} = \cancel\dfrac{34560}{1000}}}}} \\ \\ \ {\qquad{\sf{ Water \: it \: can \: Hold \: = {\red{\sf{ 34.65 \: Litres }}}}}}$

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${\orange{❒}}$ Therefore :

❝ It can hold 34.65 Litres of water in it. ❞

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Answer 2

Given:

• The circumference of the base of a cylindrical vessel is 132 cm.

• Its height is 25 cm.

To find:

• How many litres of water can it hold?

Solution :

★ Radius of the cylindrical vessel:

We know that,

Formula used :

$\\ { \underline{\boxed{\frak{ \pink{Circumference\:of\:base=2\pi\:r}}} }}$

putting values,

$\sf:\implies\:2πr = 132$

$\sf:\implies\: 2 × \frac{22}{7} × r = 132$

$\sf:\implies\: r = 132× \frac{1}{2} × \frac{7}{22}$

$\sf:\implies\: r = 21$

Radius of the cylindrical vessel is 21 cm.

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★ Volume of cylindrical vessel,

Formula used :

${ \underline{\boxed{\frak{ \red{Volume\:of\: cylinder=\pi\:r^2h}}}}}$

putting values,

$\sf:\implies\: πr²h$

$\sf:\implies\: \frac{22}{7} × 21×21 × 25 \: cm {}^{3}$

$\sf:\implies\: 22×3×21×25 \: cm{}^{3}$

$\sf:\implies\: 34650 \: cm^{3}$

$\sf:\implies\: 34.65 \: L$

Therefore, it can hold 34.65 L.