Question

Please help

Answer 1

You are planning to make an open rectangular box from an 8-by-15 in piece of cardboard by cutting congruent squares from the corners and folding up its sides. What are the dimensions of the box of largest volume you can make this way and what is it its volume?

Answer 2

I hope I'm drawing this right. So it's a rectangle with 4 small squares in each corner

Answer 3

If so, let's name the side of the square X.

Since one side is 8, one side is 15, and each side has 2x cut out (Because two squares are on each side)

So, that would make one side 8-2x, one side 15-2x and the other x (After you fold it up), right?

Answer 4

Yeah that kinda makes sense

Answer 5

@FortyTheRapper

Answer 6

So we have three sides. How would we construct the volume (l x w x h)?

Answer 7

Ugh..I'm jot sure I'm really bad at related rates/optimization

Answer 8

Not

Answer 9

Since the volume is multiplying 3 sides, we would do that

x(15-2x)(8-2x)

See where that part came from?

Answer 10

I'm sorry I had to go and I just got on not to long ago @fortytherapper

Answer 11

maximize \[V(x)=x(15-2x)(8-2x)\] as above

Answer 12

I still don't quite understand how we got there let me look back quick at the explanation

Answer 13

Here's a diagram of the box.

Answer 14

Before folding, the cardboard slab was marked like this.

Answer 15

Oh basically your subtracting two because of the Boxes so that's why it's 2x?

Answer 16

@zepdrix

Answer 17

You have to cut x out of each side.

Get a sheet of paper, measure the length and width, make four 2 inch cuts and fold up to get a "box." Measure the resulting length and width after you do that.

Answer 18

Hmmmm

Answer 19

Ugh I'm just not understanding

Answer 20

Thank you for the help everyone :)