Can someone help me solve this related rates question: Water is flowing at the rate of 60pi ft^3/min from a conical reservoir of base radius 20 ft and height 12 ft. A.) How fast is the water falling when the water is 9 ft deep? B.) How fast is the radius of the water's surface changing then?

Question

Can someone help me solve this related rates question: Water is flowing at the rate of 60pi ft^3/min from a conical reservoir of base radius 20 ft and height 12 ft.  A.) How fast is the water falling when the water is 9 ft deep?  B.) How fast is the radius of the water's surface changing then?

kira_yamato · Answer

Key: V = volume of H2O, r = radius of surface of H2O, h = ht of H2O

Attached is a sketch of the cross section of the cone

kira_yamato · Answer

(A)

kira_yamato · Answer

I mean rate of change of height is the value in the 2nd picture. And part B: