Squares of side x units are cut of the corners of a square piece of cardboard of side 6 units. The sides are then folded to make an open box. Calculate the volume of the box in terms of x.
x would be the height and 6 - 2x would be the length/width.
To calculate the volume of the box in terms of x, we need to follow a step-by-step process:
1. Start with a square piece of cardboard with side length 6 units.
2. Cut off squares of side length x units from each corner of the cardboard. This removes a square from each of the four corners.
3. After cutting off the squares, the remaining shape is a rectangle with dimensions (6-2x) units by (6-2x) units. This rectangle will be the base of the box.
4. The height of the box will be x units, which is the length of the squares that were cut off.
5. The volume of a rectangular box is given by multiplying the length, width, and height. In this case, the volume can be calculated as follows:
Volume = length * width * height
= (6-2x) units * (6-2x) units * x units
= (6-2x)^2 * x cubic units
Therefore, the volume of the box in terms of x is (6-2x)^2 * x cubic units.