Don L. answered • 10/22/15
Tutor
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(18)
Fifteen years teaching and tutoring basic math skills and algebra
Hi Jhnsoajghs, you start with a flat piece of metal that has a width of W and a length of W + 2 ( the length is 2 inches longer than the width.
The formula for volume is: V = L * W * H.
What we have to do is find out what the length and width of the box is after the 4 inch squares are cut from each corner.
When we cut the 4 inch squares out, we shorten the length and with by 8 inches. As an example, if we had started with a sheet of metal that was 24 inches wide and 30 inches long, after cutting out the 4 inch squares, we would have a width of 16 inches and a length of 22 inches
For our length of W + 2, we need to shorten it by 8 inches. The length becomes W + 2 - 8 or W - 6.
For our width of W, we need to shorten it by 8 inches. The width becomes W - 8.
The height of the box is 4 inches.
We now have the values needed to find the original length and with of the sheet of metal.
Again, V = L * W * H
32 = (W - 6)(W-8)(4)
Divide both sides by 4 giving:
8 = (W - 6)(W - 8)
8 = W^2 - 14W + 48
Subtract 8 from both sides giving:
W^2 - 14W + 40 = 0
The factors of W^2 - 14W + 40 are (W - 4) and (W - 10).
The two solutions for W are W = 4 and W = 10.
We discard the solution W = 4 because it would give a negative value when the 4 inch squares are cut from each corner.
That leaves the solution W = 10
If the width of the sheet of metal is 10 inches, and the length is 2 inches longer than the width, the length of the sheet of metal 10 + 2 or 12 inches long.
To check, we need to subtract 8 inches from the length and width of the sheet of metal. This gives the length after removing 8 inches of 4 inches. The width after removing 8 inches becomes 2 inches.
Using the formula for volume:
V = 4 * 2 * 4
V = 32 cubic inches.
Questions?
