Question

A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 l/sec. How much time req to empty half the tank, if it is 3 m in diameter/(take pie=22/7)​

Answer 1

Answer:

$16\:min\:30\:sec$

Step-by-step explanation:

Given :-

Diameter of the tank= 3m

So, radius = $\frac{3}{2} m=1.5m$

Rate of flow of water = $\frac{25}{7} l/sec$

So what is the volume of a hemisphere ?

$\frac{2}{3} \pi r^{3}$

Using it to find the volume of the tank :-

$\frac{2}{3}\pi r^{3} \\\\\ = \frac{2}{3} *\frac{22}{7} *\frac{3}{2} *\frac{3}{2}*\frac{3}{2}$

After calculating it we will get the result as :

$\frac{99}{14} m^{3}$

According to the problem :-

Volume to be emptied = $\frac{1}{2} *Volume \: of \: the\: tank$

$=\frac{1}{2} *\frac{99}{14} \\\\=\frac{99}{28}m^{3}$

WE know :-

1 meter cube = 1000 litres

So, $\frac{99}{28} m^{3} = \frac{99000}{28} l$

Time taken to empty the tank = $\frac{Volume\: in\: litre}{rate \:of \: water}$

$=\frac{\frac{99}{28} *1000}{\frac{25}{7} }$     {$\frac{l}{l/sec}=sec$}

$=\frac{99*1000*7}{25*28} \\\\=\frac{990}{60} [Dividing\: by\: 60\: to\: convert \: it into \:minutes]\\\\=16.5 \:min\\\\=16\:min\:30\:sec$

Hope It Helped You !

Answer 2

⬆️Answer is in the Attachment⬆️