SOLUTION: An open box is to be constructed from a square piece of sheet metal by removing a square of siding 5inches from each corner and turning up the edges. If the box is to hold 125 cubi

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Question 519560: An open box is to be constructed from a square piece of sheet metal by removing a square of siding 5inches from each corner and turning up the edges. If the box is to hold 125 cubic inches, what should be the dimensions of the sheet metal?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the sides of the square = x.
Then the dimensions of the base of the constructed box will be:
%28x-10%29 by %28x-10%29 and its height will be 5.
You can express the volume of the constructed box by:
V+=+%28x-10%29%28x-10%29%2A5 Substitute V+=+125 as the desired volume of the box.
125+=+%28x-10%29%28x-10%29%2A5 After simplifying, rearrange into a standard-form quadratic equation.
x%5E2-20x-25+=+0 Do you see how we got this? Solve using the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a:
x+=+%28-%28-20%29%2B-sqrt%28%28-20%29%5E2-4%281%29%28-25%29%29%29%2F2%281%29 You can work this out using your calculator. You'll get two answers only one of which will be valid.
x+=+10%2B5%2Asqrt%285%29 or 10-5%2Asqrt%285%29 These are the "exact" answers.
x+=+21.1803398875 or x+=+-1.1803398875 Discard the negative solution as the length of the side can only be a positive value.
So the original sheet metal square is 21.2 inches (approx.) on each side.