SOLUTION: How can I find the equation for the next problem: from each corner of a square piece of sheet metal, remove a square of side 9 centimeters. Turn up the edges to form an open box.

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Question 1052270: How can I find the equation for the next problem: from each corner of a square piece of sheet metal, remove a square of side 9 centimeters. Turn up the edges to form an open box. If the box is to hold 144 cubic centimeters, what should be the dimensions of the piece of sheet metal?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sides will be equal
Let +x+ = the length of a side of the
square piece of sheet metal in cm before
the corners are cut out.
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The sides after cutting out corners:
+x+-+2%2A9+=+x+=+18+ cm
The area of the bottom is:
+%28+x+-+18+%29%5E2+
The volume of the open box is:
+9%2A%28+x+-+18+%29%5E2+
+9%2A%28+x%5E2+-+36x+%2B+324+%29+=+144+
+x%5E2+-+36x+%2B+324+=+16+
Complete the square
+x%5E2+-+36x+=+-+308+
+x%5E2+-+36x+%2B+%2836%2F2%29%5E2+=+%2836%2F2%29%5E2+-+308+
+x%5E2+-+36x+%2B+324+=+324+-+308+
+%28+x+-+18+%29%5E2+=+4%5E2+
+x+-+18+=+4+
+x+=+22+
The sheet metal should be 22 x 22 cm2
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check:
+9%2A%28+x%5E2+-+36x+%2B+324+%29+=+144+
+9%2A%28+22%5E2+-+36%2A22+%2B+324+%29+=+144+
+484+-+792+%2B+324+=+16+
+808+-+792+=+16+
+16+=+16+
OK