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An open box is to be made out of a piece...

An open box is to be made out of a piece of a square card board of sides 18 cm by cutting off equal squares from the corners and turning up the sides. Find the maximum volume of the box.

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To find the maximum volume of an open box made from a square cardboard of sides 18 cm, we will follow these steps: ### Step 1: Define the variables Let \( x \) be the length of the side of the square cut from each corner of the cardboard. The dimensions of the box will then be: - Length = \( 18 - 2x \) - Width = \( 18 - 2x \) - Height = \( x \) ...
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