(Solution Library) To estimate the amount of amount of wood in the trunk of a tree, it is reasonable to assume that the trunk is a cutoff cone. If the upper radius
Question: To estimate the amount of amount of wood in the trunk of a tree, it is reasonable to assume that the trunk is a cutoff cone. If the upper radius is r and the lower radius is R ( R > r ) and the height is H , the volume of the wood is given by
\[V=\frac{\pi }{3}H\left( {{R}^{2}}+rR+{{r}^{2}} \right)\]Suppose that r , R and H are increasing at rates of 4 in/y. 5 in/y and 9 in/y, respectively. At what rate is V increasing when r = 2, R = 3 and H = 15?
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