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A coffeepot has the shape of a cylinder with radius 5 inches, as shown in the figure
above. Let h be the depth of the coffee in the pot, measured in inches, where h is a
function of time t, measured in seconds. The volume V of coffee in the pot is
changing at the rate of -5P~ cubic inches per second. (The volume V of a cylinder
with radius r and height h is V - 7rr2h. )
(a) Show that ~ = -5~ .
(b) Given that h - 17 at time t = O, solve the differential equation ~ = -5~ for
h as a function of t.
(c) At what time t is the coffeepot empty?
[ I : dV , -57r~
3 : I : computes ~
1 : shows result
(a) V - 257rh
1 : separates variables
1 : antiderivatives
1 : constant of integration
1 : uses initial condition h - 17
when t - O
1 : solves for h
max 2/5 1-1-O-O-O if no constant
O/5 if no separation of variables
~dh - - -5 dt
2JTk - O + C
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