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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1 hour

120 minutes

100 minutes

50 minutes

answer is C.

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Detailed Solution

It is given,
Internal diameter of pipe = 20cm
Diameter of cylindrical tank = 10m
Height of the tank = 2m
Water flows through the pipe at the rate of 3 km/h.
We know, 1m = 100cm
So, its radius is;

⇒ r 1 = 202 ⇒ r 1 = 10 c m ⇒ r 1 = 10100 m ⇒ r 1 = 110 m

This pipe is connected to a cylindrical tank of 10m diameter and is 2m deep.
i.e., its radius is;

⇒ r 2 = 102 ⇒ r 2 = 5 m

its height is;

⇒ h 2 = 2 m

Water flows through the pipe at the rate of 3km/h.
Time taken by the pipe to fill the tank.
Consider the pipe is in the form of cylinder with length of h1 meters.
Now, volume of pipe = volume of cylindrical tank
Using the formula for volume of a cylinder =

π r 2 h

We get,

π r 1 2 h 1 = π r 2 2 h 2

We know, 1km = 1000m
Substituting the values, we get

⇒ π 1102 h 1 = π (5) 2 × 2 ⇒ 1100 × h 1 = 25 × 2 ⇒ h 1 = 50 × 100 ⇒ h 1 = 5000 m = 5 k m

Now, since the water in the pipe flows at the rate of 3 km/h
So, the time taken by the water to travel 3km in a pipe = 1 hour = 60 minutes
Therefore, the time taken by water to travel 5km in a pipe is,