SOLUTION: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 5 cubic feet per minute. Find the rate of change of the de

Question 1186841: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 5 cubic feet per minute. Find the rate of change of the depth of the water when the water is 6 feet deep.

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
.
A conical tank (with vertex down) is 10 feet across the top and 12 feet deep.
Water is flowing into the tank at a rate of 5 cubic feet per minute.
Find the rate of change of the depth of the water when the water is 6 feet deep.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                 S t e p   b y   s t e p



(1)  The formula for the tank radius as the function of the depth is

         R = .     (1)


     Indeed, it gives the radius  R = 5 ft, when H = 12 ft.



(2)   The formula for the volume of the tank

          V =  =     (2)

       after substituting (1).



(3)  Differentiate it 

           = .



(4)  Substitute H(t) = 6 feet and  = 3.14159265

            =  = .



(5)  Substitute   = 5 cubic feet per minute

           5 = .



(6)  From this, find

             =  = 0.254647909  feet per minute.



(7)  Round and get the ANSWER:  the rate of change of the depth of the water 
     is  0.25465 feet per minute when the water is 6 feet deep.

Solved.

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