Page 28 - How To Solve Word Problems In Calculus

Substituting into the result of step 2, we get

32 − πr 2
V(r) = πr 2
πr

2
= r(32 − πr )
V(r) = 32r − πr 3

EXAMPLE 10
Water is stored in a tank in the shape of an inverted cone of
height 10 ft and diameter 6 ft. Express the volume of water in
the tank as a function of the height h of the water level.

Solution
Step1

6

r
10

h

Step2
The water is in the shape of a cone within the conical
tank. Its volume is represented by V.

π 2
V = r h
3
Step3
To obtain a relationship between r and h we use basic
geometry. Viewing the problem from a two-dimensional

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