Question

diameter of a cylinder tank is 7 m. if 385 cu. m. water is filled in the tank, then what will be the height of water in the tank?​

Answer 1

GiveN:-

Diameter of a cylinder tank is 7 m. if 385 cu. m. water is filled in the tank.

To FinD:-

Then what will be the height of water in the tank?

SolutioN:-

• Let the height of the tank be h.

We know that,

$\large{\green{\underline{\boxed{\bf{Volume\:of\:Cylinder=\pi\:r^2h}}}}}$

where,

• π is 22/7
• r is radius = diameter/2 = 7/2 m.
• h is height = ?
• Volume = 385 m³

Putting the values,

$\large\implies{\sf{385=\dfrac{22}{7}\times\left(\dfrac{7}{2}\right)^2\times\:h}}$

$\large\implies{\sf{385=\dfrac{22}{7}\times\dfrac{7}{2}\times\dfrac{7}{2}\times\:h}}$

$\large\implies{\sf{385=\dfrac{\cancel{22}}{\cancel{7}}\times\dfrac{\cancel{7}}{\cancel{2}}\times\dfrac{7}{2}\times\:h}}$

$\large\implies{\sf{385=11\times\dfrac{7}{2}\times\:h}}$

$\large\implies{\sf{385=\dfrac{11\times7}{2}\times\:h}}$

$\large\implies{\sf{385=\dfrac{77}{2}\times\:h}}$

$\large\implies{\sf{\dfrac{385\times2}{77}=h}}$

$\large\implies{\sf{\dfrac{770}{77}=h}}$

$\large\implies{\sf{\dfrac{\cancel{770}}{\cancel{77}}=h}}$

$\large\implies{\sf{10=h}}$

$\large\therefore\boxed{\bf{Height=10\:m.}}$

The height of the tank is 10 m.

Answer 2

Given Information:

• The diameter of a cylinder tank = 7 m

• If 385 m³ water is filled in the tank.

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Need To Find Out:

• The required height of water in the tank = ?

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$\sf \: Radius = \dfrac{Diameter}{2} \\ \\ \sf \: Radius = \frac{7}{2 \: } \: m$

$\underline{ \green\bigstar \bf \: Formula \: used \: here: - }$

$\underline{\boxed{\sf{ \red{Volume \: of \: the \: cylinder = \pi \: r {}^{2} \times height}}}} \: \pink \bigstar$

$\underline{ \green\bigstar \bf \: Putting \: the \: values: -} \\ \\ : \implies \sf \: 385 = \dfrac{22}{7} \times \bigg( \dfrac{7}{2} \bigg) {}^{2} \times height \\ \\ : \implies \sf \: 385 = \dfrac{22}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \times height \\ \\ : \implies \sf \: 385 = 11 \times \dfrac{7}{2} \times height \\ \\ : \implies \sf \: 385 = \dfrac{77}{2} \times height \\ \\ : \implies \sf \: Height = \dfrac{385 \times 2}{77} \\ \\ : \implies \sf \:Height = \cancel\dfrac{770}{77} \\ \\ : \implies \sf \: \boxed{ \bf \: Height = 10 \: m} \: \pink\bigstar$

$\therefore \underline {\sf \purple{\: The\: required \: height \: of \: the \: tank = \underline\bold{ \red{10 \: m}}}}$

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