An inverted right circular cone with height 30 cm and base radius 15 cm is being…
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An inverted right circular cone with height 30 cm and base radius 15 cm is being filled with water at a constant rate. Which of the following best describes how the rate at which the water level rises changes as the depth of the water increases?
(a) dh/dt decreases as h increases because each extra centimeter of depth requires more volume.
(b) dh/dt remains constant since the inflow rate dV/dt is constant.
(c) dh/dt increases with depth because the growing column of water is heavier and pushes the surface upward faster.
(d) dh/dt first increases and then decreases because the cone widens and then narrows.