Water flows at the rate of 5 m per minute through a cylindrical pipe, whose diameter is 7 cm. how long it will take to fill the conical vessel having base diameter 21 m and depth 12 m?

It will take 1200 hrs to fill the vessel.

Step-by-step explanation:

Given:

diameter of the base of the conical vessel = 21 m

radius of the base of the conical vessel r =

height of the conical vessel = 12 m

Now we know the formula of Volume of conical vessel

volume of the conical vessel =  

Substituting the values we get;

volume of the conical vessel =

Also Given:

Diameter of Cylindrical pipe = 7 cm

Radius of  Cylindrical pipe =

Now we know that 1 cm = 0.01 m

Hence  Radius of  Cylindrical pipe =

Let the conical vessel is filled in x minutes.

Then, length if the water column =

Hence water column forms a cylinder of length and radius

So, Volume of water that flows in x minutes is given by =

Volume of Water that flows in x minutes =

We will find the value of x by saying volume of the conical vessel is equal to Volume of Water that flows in x minutes.

Hence,

Since 1 hour = 60 min

Hence it will take 1200 hrs to fill the vessel.