Q. 93.9( 327 Votes )

# 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 :

As we know that 1m = 100cm

Therefore,

Radius (*r _{1}*) of circular end of pipe =

= 0.1 m

Area of cross-section =π × r_{1}^{2}

= π × (0.1)^{2}

= 0.01 π m^{2}

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 m^{3}

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

Radius (*r _{2}*) of circular end of cylindrical tank =

= 5 m

Depth (*h _{2}*) 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 ×(*r _{2}*)

^{2}×

*h*

_{2}*t*× 0.5 = (5)^{2} ×2

*t* = 100

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

Rate this question :