SOLUTION: An open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic fee
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Question 159763: An open box is to be constructed from a square piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An open box is to be constructed from a square piece of sheet metal by removing
a square of side 1 foot from each corner and turning up the edges.
If the box is to hold 4 cubic feet, what should be the dimensions of the sheet metal?
:
We know the height of the box = 1 ft
;
The dimensions of the square piece of sheet metal: x by x
The dimensions of the box will be (x-2) by (x-2) by 1
:
Quite simple really.
:
Square base * 1 ft height = 4 cu ft
(x-2)^2 * 1 = 4
x^2 - 4x + 4 = 4
x^2 - 4x + 4 - 4 = 0
x^2 - 4x = 0
x(x - 4) = 0
Two solutions
x = 0
and
x = 4 ft by 4ft is the dimensions of the sheet metal
:
Check:
Box will be: (4-2) * (4-2) * 1 = 4 cu ft
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