This is one of the most important question from the cbse board exam point of view because in 2012 and 2009 cbse board exam this question was asked. Question number 20 from RS Aggarwal book page number 811 , exercise 17B, chapter volume and surface area of solid.

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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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Given,

Diameter = 3m = 300 cm

radius( r) = 300/2 cm = 150 cm

Volume of water = volume of hemisphere = [2/3] Ï€ rÂ³

= [2/3] * Ï€ * 150*150*150

Half of the volume = (1/3 * Ï€ * 15 * 15 * 15 * 1000) cmÂ³

= (2475 * 10^4) /7 cmÂ³

Since 1000 cmÂ³ = 1 litre

= (2475*10^4) /7 cmÂ³

= 2475*10^4) / 7000

= 24750/7 litre

Since , 25/7 litre is emptied in 1 second

24750/7 litre will be emptied in(24750*7)/25*7 seconds

=990 seconds

=Â 16 min 30 sec