Sum

A hemispherical tank of radius 1.75 m is full of water. It is connected with a pipe which empties the tank at the rate of 7 litres per second. How much time will it take to empty the tank completely?

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#### Solution

Radius of the hemispherical tank = 1.75 m

Volume of the tank = `2/3pi"r"^3` cu.units

= `2/3 xx 22/7 xx 1.75 xx 1.75 xx 1.75`

= `2/3 xx 22/7 xx (175 xx 175 xx 175)/(100 xx 100 xx 100) "m"^3`

= `2/3 xx 22/7 xx 7/4 xx 7/4 xx 7/4`

= `(11 xx 49)/(3 xx 4 xx 4) "m"^3`

= `(11 xx 49)/48 "m"^3`

= `(11 xx 49)/48 xx 1000` litres

= 11229.17 litres

Time taken = `(11229.17)/7`

= 1604.17 seconds

= 26.74 minutes

= 27 minutes ...(approximately)

Concept: Volume of a Sphere

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