Barrons AP Calculus - David Bock

At the instant in question, u = 6, v = 8, and z = 10, so

EXAMPLE 37

The diameter and height of a paper cup in the shape of a cone are both 4 inches, and water is
leaking out at the rate of cubic inch per second. Find the rate at which the water level is
dropping when the diameter of the surface is 2 inches.
SOLUTION: See Figure N4–22. We know that and that h = 2r.

Here,

at any time.

When the diameter is 2 in., so is the height, and The water level is thus dropping at the
rate of in./sec.

FIGURE N4–22

EXAMPLE 38
Suppose liquid is flowing into a vessel at a constant rate. The vessel has the shape of a
hemisphere capped by a cylinder, as shown in Figure N4–23. Graph y = h(t), the height (= depth)
of the liquid at time t, labeling and explaining any salient characteristics of the graph.