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Was this done correctly? 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 . 1