A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.5 m3/min. How fast is the water level rising when it is 1.1 m from the bottom of the tank? (Round your answer to three decimal places.)

Explanation:

It is known that general formula to calculate the volume of a cone is as follows.

       Volume of the cone =

and here, r =  

So,    V =

On putting the given values into the above formula we will calculate the value f h as follows.

        V =

           =

           =

Now, we will differentiate w.r.t t as follows.

                     =

It is given that water here flows at a rate of 1.5 and h = 1.1 m.

            1.5 =

            1.5 =    

              = 0.888

                             = 0.9 m/min (approx)

Thus, we can conclude that the water level is rising at a rate of 0.9 m/min.