necromanzer52 said:
Kinarth said:
necromanzer52 said:
My maths homework. Incidentally, if someone knows how the fuck I could cut 4 equal squares out of the corners of a sheet of metal, fold up the sides, and get a box, then a little help would be great.
After you cut out the squares can they be re-used or are they discarded?
If you're just using the leftover metal then I don't think it's possible (assuming it's the expected rectangle shaped sheet)
They're discarded. Also the sheet of metal is 21 x 56. I'm supposed to find the largest possible volume of the box. But this is impossible unless the sheet of metal is a perfect square.
So if your're trying to find the size of the square you have to cut out to make the largest volume, and assuming we're talking about an open top box.
Side 1 = 21 - 2x
Side 2 = 56 - 2x
Where x is the length/width of the squares removed
Therefore the volume of the box is (21-2x)(56-2x)x
Then find the derivative and solve for when it equals zero
I get 14/3 and 21
We can ignore 21 as that would leave us with a width of zero. So put 14/3 into the original volume equation to find which is the maximum volume.
So my answer would be 68600/27 or approximately 2540.740
That's how I remember doing that type of question in high school.
Anyway right now I probably should be sleeping.