RamanuJohn wins the topless box maximum volume pizza!

click image!

RamanuJohn said...

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.

RamanuJohn wins the Pizza!