A box is to be constructed from a piece of square cardboard whose perimeter is 36 inches by cutting equal squares out of the corners and then turning up the sides. Find the maximum volume of the box that can be made this way.

Answer 1

let each side of the equal squares be x inches
length of box = 24-2x
width of box = 24-2x
height of box = x

a) Volume = x(24-2x)(24-2x)

b) expand the volume equation, then take the first derivative.
Set that derivative equal to zero. You will have a quadratic equation. Take the positive answer which lies between 0 and 12

c) put the answer from b) into the volume equation and evaluate.

Therefore, after that being said, the answer is 20>o.

Hope this helped! :)

Answer 2

Btw I used an example.

Answer 3

So the answer isn't the answer for your question.

Answer 4

if the squares have size x inches, then
v = x(36-2x)^2
dv/dx = 12(x^2-24x+108)
dv/dx=0 at x=6
so the maximum volume is 3456 in^3

Answer 5

All you need to do is V=l×l×h.
(Sorry, but I'm not gonna give you the answer)

Answer 6

wow give the answer why don't you.