Mark M. answered • 03/25/16

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Let r = radius of base at time t

h = height at time t

V = volume of cone at time t

Given: dV/dt = 10

Find: dh/dt when h = 15

V = (1/3)πr

^{2}h Since 2r = 3h, r = (3/2)hV = (1/3)π[(3/2)h]

^{2}h^{} = (3/4)πh

^{3}dV/dt = (9/4)πh

^{2}(dh/dt)10 = (9/4)π(15)

^{2}(dh/dt)dh/dt = 8/(405π) ft/min