SOLUTION: the depth of fluid,H cm, in a vessel at time t minutes is given by H = 16+4t+2t^2-(t^3/16) determine the rate at which the depth is changing after 4 minutes. if the cross se

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Question 269008: the depth of fluid,H cm, in a vessel at time t minutes is given by
H = 16+4t+2t^2-(t^3/16)
determine the rate at which the depth is changing after 4 minutes.
if the cross section of the vessel is circular,of diameter 2 m, determine the rate of filling in m3 min-1,at this time.

Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!
this is a differential calculus problem using the first derivative of depth with respect to time

dH/dt = 4 + 4t - (3/16)t^2

substituting 4 for t gives a rate of 17 cm/min

the volume rate is ___ .17 pi m^3/min


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