A storage vessel consists of a right circular cylinder of height 6 m attached…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A storage vessel consists of a right circular cylinder of height 6 m attached seamlessly to the top of an inverted right circular cone of height 8 m that shares the same radius of 2 m at their junction. The vessel is initially empty. Liquid is pumped in at a constant rate of 1.2 m3/min.
(a) Write an expression for the volume of liquid in the conical portion when the liquid depth measured from the vertex of the cone is h (where 0≤h≤8).
(b) Derive a formula for dtdh while the liquid is still entirely within the conical portion.
(c) Determine the time required for the liquid to just reach the cylindrical section.
(d) Once the cylindrical section begins to fill, find the rate at which the height of the liquid in the cylindrical section is increasing when that height is 1 m.