Interactive video lesson plan for: 2003 ap calculus frq free response question ab bc #5 a coffee pot has the shape of a cylinder with r

Activity overview:

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Question S

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~
dt
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
of integration

O/5 if no separation of variables

dh h-,-
---- ----
dt 5

1 1
~dh - - -5 dt

(b)

2JTk - O + C

Note:

Note:

t-10~

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