# Maths - Algebra

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Boxes are made by cutting 8cm squares from the corners of sheets of cardboard and then folding. The sheets of cardboard are 6cm lnbger than they are wide.

width of sheet= x
length of sheet = x+6

length of finished box = (x-10)
width of finished box = (x-16)

volume of the box = 8x^2-208x+1280cm^3

Find the dimensions of the sheet of cardboard needed to make a box with a volume of 1728cm^3.

• Maths - Algebra -

so
8x^2 - 208x + 1280 = 1728
8x^2 - 208x - 448 = 0
x^2 - 26x - 56 = 0
(x-28)(x+2) = 0
x = 28 or x = -2, but x cannot be negative,

x = 28
the box is 12 wide, 18 long and 8 high

check: (12)(18)(8) = 1728

• Maths - Algebra -

12444

• Maths - differetiate culculus -

a square piece of metal 18cm in each side n made a box without a top,by cutting a square from each corner folding up d flaps to form d side.what size corner should b cut in order volume of d box as large as possible?

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