If the box has base side x and height h, then assuming the material is also a square, we have
(x+2h)^2 = 2700
v = x^2 * h = -1/2 x^3 + 15√3 x^2
dv/dx = -3/2 x^2 + 30√3 x
dv/dx = 0 at x = 20√3, so v has a maximum of 6000√3
The box is 20√3 by 20√3 by 5√3
If 2,700 cm2 of material is available to make box with square base and an open top, find the dimensions that give the largest possible volume of the box
1 answer
1 answer