SOLUTION: a square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. if the volume of the box needs to be 180.5 cubic

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Question 315485: a square piece of cardboard is formed into a box by cutting out 2-inch squares from each of the corners and folding up the sides. if the volume of the box needs to be 180.5 cubic inches, what size square piece of cardboard is needed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a square piece of cardboard is formed into a box by cutting out 2-inch squares
from each of the corners and folding up the sides.
if the volume of the box needs to be 180.5 cubic inches, what size square piece of cardboard is needed?
:
assume this is an open box they are talking about
:
Let x = length of a side of the square piece of cardboard
:
(x-4) = length and width of the box, height = 2"
:
Volume: L*W*H = 180.5
(x-4)*(x-4)*2 = 180.5
FOIL
2(x^2 - 8x + 16)= 180.5
Divide both sides by 2
x^2 - 8x + 16 = 90.25
A quadratic equation
x^2 - 8x + 16 - 90.25 = 0
x^2 - 8x - 74.25 = 0
Use the quadratic equation to find x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
in this equation: a=1; b=-8; c=-74.25
x+=+%28-%28-8%29+%2B-+sqrt%28-8%5E2-4%2A1%2A%28-74.25%29+%29%29%2F%282%2A1%29+
:
x+=+%288+%2B-+sqrt%2864+-+%28-297%29+%29%29%2F2+
:
x+=+%288+%2B-+sqrt%28361%29%29%2F2+
the positive solution
x+=+%288+%2B+19%29%2F2+
x = 27%2F2
x = 13.5 inch square cardboard required
:
:
Check solution by finding the volume
(13.5-4)^2 * 2 =
90.25 * 2 = 180.5; confirms our solution