SOLUTION: a box with no top that has a volume of 1000 cubic inches is to be constructed from a 22cm by 30cm sheet of cardboard by cutting squares of equal size from each corner, and folding

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Question 906757: a box with no top that has a volume of 1000 cubic inches is to be constructed from a 22cm by 30cm sheet of cardboard by cutting squares of equal size from each corner, and folding up the flaps. What size square should be cut from each corner?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Your question is posted two times. For now, I am responding to this one but not the previous one. Watch the units carefully. Decide if you want to work in inches or centimeters. You might want to try solving purely in symbolic form and then take care of the units as part of the substitution solving stage.

If x is the length of the side of the square to cut from each corner, and if you want u and v to be "length" and "width" of the original rectangle, then the VOLUME may be represented as x%28u-2x%29%28v-2x%29; and maybe converting the given 1000 cubic inches into its equivalent cubic centimeters may be more comfortable, and you can expect that x will be in centimeters.

CORRECTED INFORMATION PROVIDED----- 1000 cubic centimeters, NOT inches

That helps. Here is how to start:

The base dimensions will be 22-2x and 30-2x.
Area of the base: %2822-2x%29%2830-2x%29
VOLUME of the box: highlight_green%28x%2822-2x%29%2830-2x%29=1000%29.

Simplify the volume equation and ... solve for x. There maybe be "three" solutions but you may need to choose the SENSIBLE solution.

The steps done separately on paper yielded highlight%28x%5E3-26x%5E2%2B165x-250=0%29; not the finished answer, but an important step in that direction.