SOLUTION: See Figure N4–21. Let u, v, and z denote the lengths respectively
of AB, AC, and BC. We know that and . Since (at any time) z^2
= u^2 + v^2 , then
.At the instant in question, u = 6, v = 8, and z = 10, soExample 35 __
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.
When the diameter is 2 in., so is the height, and . The water level is thus
dropping at the rate of in./sec.