An inverted right circular cone (point down) has a height of 10 m and a base radius of 5 m
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An inverted right circular cone (point down) has a height of 10 m and a base radius of 5 m. Water flows into the cone from a pump at a constant rate of 2.0 m3\,/min. A valve at the vertex allows water to drain from the tank at a constant rate of 1.0 m3\,/min.
At the instant when the water is exactly 3.0 m deep, answer the following questions.
(a) Express the volume V of water in the tank as a function of the water depth h. Include correct units.
(b) Compute the instantaneous rate of change of the water depth dtdh at the instant described. State the units of your result and indicate whether the water level is rising or falling.
(c) Interpret the physical meaning of the sign and magnitude of your answer in part (b) within the context of the filling and draining processes occurring simultaneously.