A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?

Explanation

To find the side of the square to be cut off from each corner of a square piece of tin of side 18 cm, so that the volume of the box formed is maximized, we can follow these steps:

### Step 1: Define the variables
Let \( x \) be the side length of the square cut from each corner. After cutting out squares from each corner and folding up the sides, the dimensions of the box will be:
- Length = \( 18 - 2x \)
- Width = \( 18 - 2x \)
- Height = \( x \)

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