Question

9. 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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Answer 1

Step-by-step explanation:

I hope it will be help full for you

Answer 2

Answer:

• in 100 minutes the tank will be filled.

Given:-

• internal diameter of pipe = 20cm.
• diameter of cylindrical tank = 10m.
• height = 2m.
• rate of flow of water from pipe = 3 km/h.

step-by-step solution:-

First let us find find the volume of pipe,

⟶ internal diameter is 20 cm

⟶ So we get the radius as r = d / 2 = 20 / 2 = 10 cm = 1 / 10 m

⟶ Volume of pipe = πr²h

                           = π (1/10)² h

⟶ volume of pipe = πh/100

Now to find volume of tank which is cylindrical,

  So d = 10 m, r = d/2 = 5 m and height is 2 m

⟶  Volume of tank = πr²h

                        = π (5)² x 2

⟶   Volume of tank = 50 π

The farmer connects pipe to the tank, so

Volume of pipe = volume of tank

     

⟶  πh / 100 = 50 π

⟶  h = 50 π x 100 / π

⟶ h = 5 km

⟶ Water travels at 3 km / hr

⟶  For 3 kms the time taken for water to travel is 1 hr

⟶  So for 5 kms time taken will be 5 / 3 hrs

⟶     5 / 3 x 60 = 100 minutes

The tank will be filled in 100 minutes.