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A city is building a cyllindrical water tower. [Draw Cyllinder on board.] Due to
regulation the radius plus the height of the cyllinder has to be 500 feet. Express the
volume of the cyllinder as a function of it radius.
Solution:
Since the radius plus the height has to be 500 feet we have a constraint equation of
r + h = 500.
The volume of a cyllinder is v = 2πrh. First I will solve the constraint equation for h
and get
h = 500 − r.
Then I will plug this in for h in my fomula for volume. This gives me
v(r) = 2πr(500 − r) = 1000πr − 2πr2 .
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