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 a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Also, find the maximum volume.

Explanation

To solve the problem of maximizing the volume of an open box formed by cutting squares from the corners of a square piece of tin, we can follow these steps:

### Step 1: Define the variables
Let \( x \) be the side length of the square cut from each corner. The original square piece of tin has a side length of 18 cm.

### Step 2: Determine the dimensions of the box
After cutting out squares from each corner and folding up the sides, the dimensions of the box will be:
- Length = \( 18 - 2x \)
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