Posted by Alaina on Wednesday, February 10, 2010 at 4:15pm.
If you have only 500 sq. feet of material and have to built a swimming pool, which shape will hold the most water. A cylinder, a cube or a rectangular prisim?

Geometry  Reiny, Wednesday, February 10, 2010 at 5:27pm
Is the material used for the liner of the pool?
Is this a question from a Calculus course?
Let the base be a square, (again an assumption)
let the base by x by x feet, let the height be y feet
then x^2 + 4xy = 500
4xy = 500 x^2
y = (500  x^2)/(4x)
volume = x^2y
= x^2(500  x^2)/(4x)
= 500x^2 = x^3/4
differentiate and set that equal to zero and solve.
You will get a quadratic equation with two roots.
Discard the negative root if there is one.
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