A hemispherical tank full of water is emptied by a pipe at the rate of litres per second. How much time will it take to half empty the tank, if the tank is 3 m in diameter.

Let r m be the radius of the hemispherical tank, then

$straight r space equals space 3 over 2 straight m.$
Now, volume of hemispherical tank

$equals 2 over 3 πr cubed equals space open parentheses 2 over 3 straight x 22 over 7 straight x 3 over 2 straight x 3 over 2 straight x 3 over 2 close parentheses space straight m cubed equals space 99 over 14 straight m cubed equals 99000000 over 14 space cm cubed$
And, Volume of water to be emptied

$equals 1 half$ (Volume of hemispherical tabk)

$equals open parentheses 1 half straight x 99000000 over 14 close parentheses space cm cubed equals space 99000000 over 28 straight x 1 over 1000 space litres equals space 99000 over 28 space litres$
Hence,
Time taken to half empty the tank

$equals space 99000 over 28 straight x 7 over 25 space seconds$
= 16.5 minutes.

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