Q. 74.7( 10 Votes )

# A farmer connects a pipe of the internal diameter of 20 cm from a canal into the cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time the tank be filled?

Answer :

**Given:** Internal diameter of pipe = 20 cm

The diameter of cylindrical tank = 10 m

The height of cylindrical tank = 2 m

**Formula Used:**

Volume of cylinder = πr^{2}h

**Explanation:**

The figure for a given question is:

The internal diameter of the pipe, d = 20 cm

So, radius “r” of the pipe =

Let the length of the pipe for equalling the volume of the cylindrical tank is “h” cm.

The diameter of the cylindrical tank, D = 10 m

So, radius “R” of the cylindrical tank =

Height of the cylindrical tank, H = 2 m = 200 cm

We know that volume of a cylinder = πr^{2}h

Now,

The volume of cylindrical tank = Volume of the pipe

⇒ πR^{2}H = πr^{2}h

⇒

⇒

⇒

⇒ h = 500000 cm

⇒ h = 5 km

Now, the water flows through the pipe at the rate of 3 km/hr,

Or,

water flows 3 km through a pipe in = 1 hr

Water flows through pipe 1 km in =

Water flows through pipe 5 km in =

= 100 min ~ 1 hour 66 mins

∴ the tank will fill in 1 hour 66 mins approximately.

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