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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