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Question
The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
Solution
Given, internal diameter of a hemispherical tank = 14 m
And internal radius of a hemispherical tank, r = 7 m
Water in the hemispherical tank = 50 kL
= 50 × 1000 L ...[∵ 1 kL = 1000 L]
= 50000 L
= 50 m3 ...[∵ 1 m3 = 1000 L]
∴ Volume of water in the hemispherical tank = `2/3 pir^3`
= `2/3 xx 22/7 xx (7)^3`
= `2/3 xx 22/7 xx 7 xx 7 xx 7`
= 718.66 m3
Now, volume of water pumped in the hemispherical tank = 718.66 – 50 = 668.66 m3
Hence, the volume of water pumped into the tank is 668.66 m3.
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