A large conical tank with fixed dimensions is being filled with water at a constant…
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A large conical tank with fixed dimensions is being filled with water at a constant rate of 10 ft3/min. Which of the following best describes how the rate at which the water level (depth) rises changes as the tank becomes fuller?
(a) It increases because the cross-sectional area of the water decreases with height.
(b) It remains constant because the inflow rate of 10 ft3/min is constant.
(c) It decreases because each additional unit of height requires more volume than the previous one.
(d) It first decreases, then increases once the water passes the midpoint of the tank’s height.