SOLUTION: DIMENSIONS OF A BOX: A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown

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Question 199290This question is from textbook algebra and trigonometry
: DIMENSIONS OF A BOX: A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 100 in.^3. How big a piece of cardboard is needed? This question is from textbook algebra and trigonometry

Found 2 solutions by RAY100, checkley77:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
Volume of box is s^2 *4 =100,,,,therefore s= 5
.
net is a square with 4 x 4 corners removed,, and sides = 4 +s +4 = 13
.
or net is sheet 13 by 13
.

Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
Let x be the length of the square piece of cardboard.
(x-4*2)^2 this accounts for the two 4 in. corners cut out.
(x-8)^2 is the bottom area.
4 inches is the height.
4(x-8)^2=100
4(x^2-16x+64)=100
4x^2-64x+256-100=0
4x^2-64x+156=0
4(x^2-16+39)=0
(x-13)(x-3)=0
x-13=0
x=13 ans. for the original length of the square piece of cardboard.
Proof:
(13-8)^2=5^2=25
4*25=100
100=100