# 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?

As we know that 1m = 100cm
Therefore,

Radius (r1) of circular end of pipe =

= 0.1 m

Area of cross-section =π × r12

= π × (0.1)2

= 0.01 π m2

Speed of water = 3 km/h

=

=

= 50 meter/min

The volume of water that flows in 1 minute from pipe = 50 × 0.01 π

= 0.5π m3

The volume of water that flows in t minutes from pipe = t × 0.5π m3

Radius (r2) of circular end of cylindrical tank =

= 5 m

Depth (h2) of cylindrical tank = 2 m

Let the tank be filled completely in t minutes

The volume of water filled in the tank in t minutes is equal to the volume of water flowed in t minutes from the pipe

The volume of water that flows in t minutes from pipe = Volume of water in the tank

t× 0.5π = π ×(r2)2 × h2

t× 0.5 = (5)2 ×2

t = 100

Hence, the cylindrical tank will be filled in 100 minutes.

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