Maths Calculus
posted by Daksh on .
a sheet of cardboard is to be folded up to make a closed box. If the cardboard measures 55 cm by 80cm calculate the maximum volume of the box that can be made from this sheet of cardboard

let each side of the squares to be cut out be x cm
length = 802x
width = 552x , 0 < x < 27.5
height = x
V = x(802x)(552x)
= 4x^3 270x^2 + 4400x
dV/dx = 12x^2  540x + 4400
= 0 for a max of V
3x^2  135x + 1100 = 0
x = (135 ± √5025)/6
take it from there (I get x = appr 10.69)