Find length of square to cut from corners to create box

[ashloveskyle]

how do you solve:


find the length,x, of the square one must cut out of the corners in order for the volume of the box to equal the surface area of the outside of the box. Explain and/or show how you arrived at your answer.

volume=4x^3-88x^2+448x
surface area = -4x^2-88x+536

 

[stapel]

volume=4x^3-88x^2+448x
surface area = -4x^2-88x+536

How did you arrive that these equations?

Please be complete. Thank you!

Eliz.

 

[TchrWill]

how do you solve:


find the length,x, of the square one must cut out of the corners in order for the volume of the box to equal the surface area of the outside of the box. Explain and/or show how you arrived at your answer.

volume=4x^3-88x^2+448x
surface area = -4x^2-88x+536

Let L = the side of the square and x = the side of the corner squares.

A = 4x(L-2x) + (L-2x)^2

V = x(L-2x)^2

Then, 4x(L-2x) + (L-2x)^2 = x(L-2x)^2

Can you take it from here?