Question

A cylindrical tank has a radius of 154 cm .It is filled with water to a height of 3m.If water to height of 4.5m is poured into it , what will the increase in the volume of water in kl

Answer 1

Answer:

Step-by-step explanation:

Given,

Radius of cylindrical tank, r = 154 cm = 1.54 m

Height of water, h = 3 m

Larger height of water, H = 4.5 m

To Find,

Increase in the volume of water.

Formula or method to be used,

Increase in volume of cylinder = πr² × (H - h)

Solution,

Putting all the values, we get

Increase in volume of cylinder = πr² × (H - h)

⇒ Increase in volume of cylinder = 22/7 × 1.54² × (4.5 - 3)

⇒ Increase in volume of cylinder = 22/7 × 1.54 × 1.54 × 1.5

⇒ Increase in volume of cylinder = 22/7 × 2.3716 × 1.5

⇒ Increase in volume of cylinder = 11.1804 m³

Hence, the increase in the volume of the cylinder is 11.1804 m³.

Answer 2

${\bf{Given\::}}$

• Radius of a cylindrical tank is 154 cm.

➛ 154 cm

➛ $\tt{\dfrac{154}{100}}$

➛ 1.54 m

• Height of water level is 3 m.

• Some water to a height of 4.5 metres is poured into it.

$\\ {\bf{To\: Find\::}}$

• Increase in volume of water.

$\\ {\bf{Solution\::}}$

As we know that,

✯ Volume of the cylinder, when water level is upto 3 m, is

$\dashrightarrow\:\tt{(Volume)_1\:=\:\dfrac{22}{7}\times{(1.54)^2}\times{3}\:}$

✯ After water level increase upto 4.5 m, then it's volume is,

$\dashrightarrow\:\tt{(Volume)_2\:=\:\dfrac{22}{7}\times{(1.54)^2}\times{4.5}\:}$

Let,

• v be the increase in volume of water.

Then,

✯ Increase in volume of water is,

$:\implies\:\tt{v\:=\: (Volume)_2\:-\:(Volume)_1\:}$

$:\implies\:\tt{v\:=\:\left(\dfrac{22}{7}\times{(1.54)^2}\times{4.5}\right)\:-\:\left(\dfrac{22}{7}\times{(1.54)^2}\times{3}\right)\:}$

$:\implies\:\tt{v\:=\:\dfrac{22}{7}\times{(1.54)^2}\times{(4.5\:-\:3)}\:}$

$:\implies\:\tt{v\:=\:\dfrac{22}{7}\times{1.54}\times{1.54}\times{1.5}\:}$

$:\implies\:\tt{v\:=\:22\times{0.22}\times{1.54}\times{1.5}\:}$

$:\implies\:\bf\pink{v\:=\:11.1804\:m^3\:}$

⠀⠀⠀⠀ : Conversion into Litres :

$\dashrightarrow\:\bf{1\:m^3\:=\:1000\: Litres}$

$\dashrightarrow\:\tt{11.1804\:m^3\:=\:(1000\times{11.1804})\: Litres}$

$\dashrightarrow\:\bf{11.1804\:m^3\:=\:{\pink{11180.4\: Litres}}\:}$

∴ Increase in volume of water is 11180.4 L.