Sure, click image.
From a rectangle of thin cardboard / pasteboard measuring 31 cm x 25 cm, cut 4 equal squares from the corners. Discard the squares.
Fold up the tabs and tape the seams together to make a box with no top.
What should the length of each side of the squares be to make the box of the greatest possible volume?
You can experiment with lots of different boxes. You can fill each box to the top with salt and use the ruler to make the salt level/flat with the top of the box, and then measure the volume of the salt with the graduated cylinder.
Maybe you don't need the salt or the cylinder. Maybe you don't need the cardboard or the ruler. Maybe you don't have to actually make any boxes. Maybe you can just compute the length of the side of the squares.
(But if you can't, cardboard, salt and tape are cheap.)
4 slices with avacado and shallots.
4 comments:
Um, I know this one. Do you want the answer since you owe me so much pizza already?
yeah yeah yeah answer it if you can. We can combine 20 pieces of pizza into one full-blown fancy Italian dinner if you like.+
Um, I'm going to bow out of this one for the time being. I mis read the question late last night after a long, long day, and its more complicated than I thought. Going to take some more mental energy, that I don't currently have.
It's like this:
Volume = x * (31-2x) * (25-2x)
V = 4x^3 - 112x^2 +775x.
V' = 12x^2 -224x + 775.
x, where V' = 0, gives us the inflection points -- potential answers.
There are two solutions for x, via the quadratic formula.
One gives us negative dimensions, which does not work in my universe. (Also, our answer would be the one for which V'' is negative, where V'' = 24x - 224, for the particular value of x.)
The real-world solution for x is
(224 - SQRT(12976))/24
which is (very) roughly 4.5.
So the pizza box with the greatest volume has to be about 4.5 inches high.
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