Question

An upright cylindrical tank with radius 6 m is being filled with water at a rate of 2 m3/min. how fast is the height of the water increasing?if h is the water's height, the volume of the water is v = πr2h. we must find dv/dt. differentiating both sides of the equation gives

Answer 1

Volume = pir^2h = 36pih Derivative = 36pi dh/dt v' = 2 m^3/min 2 = 36pi dh/dt dh/dt = 0.0177 m/min.