Question

A farmer connects a pipe of internal diameter 20 cm form 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

Consider an area of cross-section of pipe as shown in the figure.

Radius (r₁) of circular end of pipe = 20/200 = 0.1 m

Area of cross-section = π r₁² = π x (0.1)² 

                                  = 0.01π m² 

Speed of water = 3 km/h =3000/60 =50 meter/min

Volume of water that flows in 1 minute from pipe 

= 50 × 0.01π = 0.5π m³ 

Volume of water that flows in t minutes from pipe = t × 0.5π m³  

Radius (r₂) of circular end of cylindrical tank =10/2 =5 m

Depth (h₂) of cylindrical tank = 2 m

Let the tank be filled completely in t minutes.

Volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.

Volume of water that flows in t minutes from pipe = Volume of water in tank

t × 0.5π = π ×(r₂)² ×h₂

t × 0.5 = 5² ×2

t = 100

Therefore, the cylindrical tank will be filled in 100 minutes.