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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?**

Answer:

Consider the following diagram-

\text{Radius}\left(r_1\right)\text{of circular end of pipe} =\frac{20}{200}=0.1\mathrm{~m}\\ \text{Area of cross-section}=\pi\times r_1^2=\pi\times(0.1)^2=0.01\pi\mathrm{m}^2\\ \text{Speed of water}=\frac{3000}{60}=50\ \text{metre/min}\\ \text{Volume of water that flows in 1 minute from pipe}=50\times0.01\pi=0.5\pi\mathrm{m}^3

Volume of water that flows in t minutes from pipe = t×0.5π m^{3}

Volume of water that flows in t minutes from pipe = t×0.5π m^{3}

Radius (r_{2}) of circular end of cylindrical tank =10/2 = 5 m

Depth (h_{2}) 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×r_{2}^{2}×h_{2}

Or,

**t = 100 minutes**

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