Question

L Aishwarya
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 1

Let the length of pipe for filling the whole tank be h m.
So, Volume of pipe = Volume of tank
Volume of pipe
Let Height = h m
Diameter = 20 cm
So, radius = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 20/2 = 10 cm = 10 × 1/100 m = 1/10 m
Volume of pipe = Volume of cylinder = 𝜋r2h = 𝜋(1/10)^2 h = 𝜋 × 1/100 × h = 𝜋ℎ/100
Volume of tank
Diameter = 10 m
Radius = r = 10/2 m = 5 m
Height = h = 2 m
Volume of tank = 𝜋r2h = 𝜋(5)^2 × 2 = 𝜋 × 25 × 2 = 50𝜋
Now, Volume of pipe = Volume of tank
𝜋ℎ/100 = 50𝜋 h = (50𝜋 ×100 )/𝜋 h = 5000 m h = 5 km
Now, Water in pipe flows at rate 3 km/hr
So, 3 km travels in pipe in = 1 hour 1 km travels in pipe in = 1/3 hr 5 km travels in pipe in = 5/3 hr = 5/3 × 60 minutes = 5 × 20 minutes = 100 minutes.
So, in 100 minutes, the tank will be filled.