SOLUTION: Differentiation
An empty open container in the shape of an inverted cone has a circular top of radius (r+3) m and a depth of h m, where r and h are constants. Water is poured in
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An empty open container in the shape of an inverted cone has a circular top of radius (r+3) m and a depth of h m, where r and h are constants. Water is poured in
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Question 1118346: Differentiation
An empty open container in the shape of an inverted cone has a circular top of radius (r+3) m and a depth of h m, where r and h are constants. Water is poured in at a constant rate of 18pie m^3/s. After t seconds, the volume of water, V in the container is at a depth of (h-1) m.
(i) Show that h=[(r+k)/k], where k is a constant to be determined. Hence, express V in terms of r.
(ii) Given that the change of the radius increasing at the rate of (2r+1) m/s, show that r satisfies the equation 2r^3 + 13r^2 + 24r - 72 = 0. Hence, find the value of r.
(iii) Find the rate at which the depth of the water is increasing when t=3. Answer by Alan3354(69443) (Show Source):
