2) The dimensions of the box are: l = 30 - 2x, w = 20 - 2x, h = x. So the volume of the box is: V = (30 - 2x)(20 - 2x)x.Originally Posted byOverclockerR520

So. The volume of the box is 1000.

I don't know where you are as far as solving cubic equations is concerned. I will simply state at this point that the solutions are x = 5, x = , and x = . If you need help with this sort of thing, just say so and I'll be happy to provide.

So which are the two we can use for the box? Remember that we are removing 2x from each dimension of the cardboard. , so we can't use that one. The other two will work.

So we have two possible boxes:

1) in

in

in

2) in

in

in

As for surface area: We have at the bottom of each box a rectangle of area (30 - 2x)(20 - 2x). We have two vertical flaps of area (30 - 2x)x and two of area (20 - 2x)x. Adding all this up we get a surface area of:

1) x = 5: SA = 500 in^2

2) : in^2

So box 1 has the smaller surface area.

-Dan