SOLUTION: The sum of the radius and height of a cylinder is 20 cm. The dimensions are whole numbers. What is the largest possible volume of this cylinder? Answer in terms of π.

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Question 1088456: The sum of the radius and height of a cylinder is 20 cm. The dimensions are whole numbers.
What is the largest possible volume of this cylinder?
Answer in terms of π.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
radius is x
height is 20-x
volume is pi*r^2*h=pi*x^2(20-x)=pi(20x^2-x^3)
maximize this
take the derivative and get -3x^2+40x, and set it equal to 0
3x^2-40x=0
factor out an x and divide by 3, moving the constant, x=40/3
whole number dimension for radius is 13 largest whole number.
height is 7 cm
volume is pi (169)*7=1183 pi ANSWER
check with height of 8 and volume of 12=1152 pi
check with height of 6 and volume of 14=1176 pi