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Question
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?
Solution
We have,
the radius of the hemispherical tank`= r=3/2 "m"`
Volume of the hemispherical tank `=2/3 pir^3`
`= 2/3xx22/7xx3/2xx3/2xx3/2`
`= 99/14 "m"^3`
Now,
Volume of half tank`=1/2 xx90/14`
`= 99/28 "m"^3`
`=99/28 "KL"`
`=99000/28 "L"`
As, the rate of water emptied by the pipe = `25/7 "L"//"s"`
so, the time taken to emty half the tank `= (99000/28)/(25/7)`
`= 99000/(25xx4)`
`= 990 s`
`= 990/60 min`
= 16.5 min
= 16 min 30 s
So, the time taken to empty half the tank is 16 minutes and 30 seconds.
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