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01/07/2021 11:29 am
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A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?
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01/07/2021 11:32 am
Radius (r1) of circular end of pipe = \(\frac{20}{200}\) = 0.1 m
Area of cross-section = \(\pi \times r_1^2 = \pi \times (0.1)^2 = 0.01 \pi m^2\)
Speed of water = 3 km/h = \(\frac{3000}{60}\) = 50 metre/min
Volume of water that flows in 1 minute from pipe = 50 x 0.01 π = 0.5π m3
Volume of water that flows in t minutes from pipe = t × 0.5π m3
Volume of water that flows in t minutes from pipe = t × 0.5π m3
Radius (r2) of circular end of cylindrical tank =10/2 = 5 m
Depth (h2) of cylindrical tank = 2 m
Let the tank be filled completely in t minutes.
Volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.
Volume of water that flows in t minutes from pipe = Volume of water in tank
= t × 0.5π = π × r22 × h2
t = 100 minutes