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A hemispherical tank , full of water , is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m ?

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Radius=3/2 m

volume of hemisphere=2/3 πr³

=2/3 * 22/7 * (3/2)³ =99/14 m³

vol. of water that would be emptied=1/2 of vol.of hemispherical tank

=1/2 *99/14 =99/28 m³

vol.=99/28 m³ *1000 litres

=99000/28 litres

in 1 second as 25/7 litres of water would be emptied

so,99000/28 litres of water would be emptied in =99000/28 *7/25

=3960/4

=990 seconds

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Given,

Diameter of Hemispherical Tank=3m

So, Radius of Hemispherical Tank=3/2m

Volume of Hemispherical Tank=2/3πr3

=2/3*22/7*3/2*3/2*3/2

On solving, We get Volume of Hemispherical Tank= 99/14m3

Half the volume of Tank= 99/28m3

Now, 1m3=1000 Liters

99/28m3=99000/28 Litres

This Implies, if 25/7 litres of water is emptied in 1sec,

So, 1 Litres of water will be emptied in 7/25 sec  (Unitary Method of solving)

So, 1/2 the volume of Hemispherical Tank i.e.99000/28 Litres will be emptied in:

99000/28*7/25

Which is equal to=990 seconds or 16 Minutes 30 seconds.........

Hope, My answer is correct and You will understand it Easily!!

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