Question

A hemispherical tank is emptied by a pipe at the rate of 11 litres per second. How long will it take to half empty the tank if it is 1.4 m in diameter. (Take 22/7)

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

• The rate of emptying the hamisperhrical tank = 11 L / sec .

• The diameter of the hemispherical tank = 1.4 m .

$\LARGE\textbf{\underline{\underline{To find :-}}}$

• Time required to empty the half tank = ?

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

$\large\boxed{\texttt\textcolor{purple}{:↦ Volume of a hemisphere = \cfrac{2}{3}\pi r ^ { 2 } }}$

$\LARGE\textbf{\underline{\underline{Method :-}}}$

• First we have to find the volume of the hemispherical tank , volume means the capacity of the tank to hold the water .

• Then we have to half the volume of tank and then divide it by the rate of emptying the tank .

• By doing this steps we would get the answer to the Question .

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

• We have to find the volume of the tank by using the formula of the ' volume of the hemisphere ' .

➩ Here :-

• π = 22 / 7

• r = D / 2

= 1.4 / 2

• r = 0.7 m

$\large\texttt{↦ Volume = \cfrac{2}{3} × \cfrac{22}{7} × ( 0.7)³ }$

$\large\texttt{↦ Volume = \cfrac{2}{3} × \cfrac{22}{\cancel7} × \cancel{0.343 } }$

$\large\texttt{↦ Volume = \cfrac{2}{3} × 22 × 0.049 }$

$\large\boxed{\texttt\textcolor{red}{↦ Volume of the tank = \cfrac{2.156}{3} }}$

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• As the volume can't be divided further we have to keep it as it is .

• Now we have to divide the calculated volume by 2 so that we can get the half volume of the tank .

• So ,

$\large\texttt{↦ Half volume of the tank = \cfrac{2.156}{3} × {1}{2} }$

$\large\texttt{↦ Half volume of the tank = \cfrac{\cancel{2.156}}{3} ×\cfrac {1}{\cancel2} }$

$\large\boxed{\texttt{\textcolor{red}{↦ Half volume of the tank = \cfrac{1.078}{3} }}}$

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• As we have calculated the half volume of the tank we have to divide it be the rate of emptying .

• The rate of emptying is 11 L / sec .

$\large\texttt{↦ Time required = \cfrac{\cancel{1.078}}{3} × \cfrac{1}{\cancel{11}} }$

$\large\boxed{\texttt{\textcolor{red}{↦ Time required = \cfrac{0.098}{3} \: \: seconds }}}$

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