Question

A cylindrical water tank of diameter 2.8 m and height 4.2 m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4 m s^–1. Calculate, in minutes, the time it takes to fill the tank.

Answer 1

Diameter of cylindrical tank = 2.8 m

Therefore, radius = 1.4 m

Height = 4.2 m

Volume of water filled in it = πr²h 

= `22/7 xx 1.4 xx 1.4 xx 4.2  m^3` 

= `181.104/7m^3` 

= 25.872 m³      ...(i) 

Diameter of pipe = 7 cm 

Therefore, radius (r) = `7/2` 

Let length of water in the pipe = h₁ 

∴ Volume = πr²h₁ 

= `22/7 xx 7/2 xx 7/2 xx h_1` 

= `77/2 h_1 cm^3`    ...(ii) 

From (i) and (ii)   

`77/2 h_1 cm^3 = 25.872 xx 100^3 cm^3` 

`=> h_1 = (25.872 xx 100^3 xx 2)/77`  

`=> h_1 = (25.872 xx 100^3 xx 2)/(77 xx 100)`  

`=>` h₁ = 0.672 × 100²m

`=>` h₁ = 6720 m  

Therefore, time taken at the speed of 4 m per second 

= `6720/(4 xx 60)` minutes

= 28 minutes