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Question
A hemispherical tank, full of water, is emptied by a pipe at the rate of `25/7`litres per sec.
How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?
Solution
It is given that, diameter of base of tank = 3 m
`therefore Redius,r=3/2m`
Volume of water in the hemispherical tank
`=2/3pir^3`
`=2/3xx22/7xx(3/2m)^3`
`=99/14m^3`
Rate of flow of water out of the pipe =`25/7`litres / sec
Let the time taken to empty half the tank be t sec.
∴ Rate of flow of water × t sec `=1/2xx`Volume of water in the hemispherical tank
`rArr25/7xxt litre=1/2xx99/14m^3`
`rArr 25/7xx1/1000xxt m^3=1/2xx99/14m^3` `(therefore l litre = 1/1000m^3)`
`thereforet=990`
∴ Time taken to empty half the tank is (960 + 30) sec = 16 min 30 sec
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