SOLUTION: A rectangular piece of stainless steel sheet metal measures 8 meters by 10 meters. if we are to take an open-top tank by cutting equal squares from each corner, folding up the tabs

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Question 1171508: A rectangular piece of stainless steel sheet metal measures 8 meters by 10 meters. if we are to take an open-top tank by cutting equal squares from each corner, folding up the tabs by 90 degrees, and welding the vertical edges; what size should the squares be cut to have the container hold 48 cubic meters?
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Edge length of each cut square, x.

Base area, %288-2x%29%2810-2x%29
and height of box is x.

x%288-2x%29%2810-2x%29=48
.
.
.
%28x-2%29%28x-1%29%28x-6%29=0
.
.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Draw this.
the width will be 8-2x, where x is how much is cut in meters
the length will be 10-2x
the height will be x
the volume is x(80-36x+4x^2)=48
or 4x^3-36x^2+80x-48=0
or x^3-9x^2+20x-12=0
/1== -9== 20== -12
1--- -8---12----0 so the factors are (x-1)(x^2-8x+12)=(x-1)(x-6)(x-2)
the graph shows x=1,2,6, as well. The last is too large and leads to negative values
1 meter on each side would give dimensions of 8*6*1. And 2 meters on each side 4*6*2. Both of these would give 48 m^2.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3-9x%5E2%2B20x-12%29