Page 71 - How To Solve Word Problems In Calculus

Solution
Step1
5

r
20

h

Step2
Let V represent the volume of water in the tank. The vol-
3
ume is increasing at the rate of 100 ft /min.
dV dh
Given: = 100 Find: when h = 10
dt dt
Step3
The relationship between V, r, and h is given by the for-
mula for the volume of a cone:
π
2
V = r h
3
Since we are given no information about r or dr/dt, it is best
to eliminate r from this equation. This is accomplished by
observing the cone from a D 5 E
two-dimensional perspective.
By observing that
ABC is
similar to
ADE in the diagram
to the right, we see that r
B C
h 20 20
=
r 5
h
20r = 5h

h
r = A
4
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