Question

A FARMER CONNECT A PIPE OF INTERNAL DIAMETER 20CM FROM A CANAL INTO A CYLINDIRICAL TANK IN HER FIELD WHICH IS 10 CM IN DIAMETER AND 2 M DEEP IF WAYER FIOWA THROUGH THE PIPE AT THE RATE OF 3 KM/H IN HOW MUCH TIME WILL THE TANK BE FILLED?

Answer 1

Let the time taken be x.

Therefore flow of water in pipe in x hrs = 3x km
⇒ length of water column is 3x km = 300000 cm

diameter of pipe is 20 cm
∴ radius = 10cm

diameter of tank is 10 m 
∴ radius is 5 m

also, depth of tank is 2 m = 200cm

∵ The water is poured into the tank
∴ volume of pipe = volume of tank
⇒r₁²h₁ = r₂²h₂
⇒10 *10 * 300000x = 500 * 500 * 200
⇒x = 50/30
⇒x =5/3 hr 
      = 5/3 *60
      = 100 mins

Answer 2

let time taken be "t"
first we must find the area of cross section of pipe=π r2
=π *10*10
= 100π ------1

3 km/h=3*1000/60 (in terms of meter)

volume of cylinder=π r2h
=π *5 *5*2
=50π-----------2

now volume of cylinder=speed * area of cross section of pipe
50π = 3 *1000/60 *100π
=50*2 
=100
 thus time taken by the pipe to fill the cylindrical tank =100 minutes.

hope it helps!!!!