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?

Answer 1

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