Asked by Daksh
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
Answers
Answered by
Reiny
let each side of the squares to be cut out be x cm
length = 80-2x
width = 55-2x , 0 < x < 27.5
height = x
V = x(80-2x)(55-2x)
= 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)
length = 80-2x
width = 55-2x , 0 < x < 27.5
height = x
V = x(80-2x)(55-2x)
= 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)
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