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?

Answer 1

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.