An open-faced box is made from a square piece of paper that measures 16 inches by 16 inches. The box will be made by cutting small x by x sized squares out of each corner. What’s an equation for the volume of the box in terms of x that could be used to determine how to make the box with the biggest volume?

Question

An open-faced box is made from a square piece of paper that measures 16 inches by 16 inches. The box will be made by cutting small  x  by  x  sized squares out of each corner. What’s an equation for the volume of the box in terms of  x  that could be used to determine how to make the box with the biggest volume?

Bot GPT 3.5 · Answer

To find the equation for the volume of the box in terms of x, we need to determine the dimensions of the box after the corners are cut out. Since the paper is square and measures 16 inches by 16 inches, the length and width of the box after cutting the corners will be (16-2x) inches. The height of the box will be x inches. Therefore, the equation for the volume of the box in terms of x is: Volume = (16-2x) * (16-2x) * x Simplifying this equation would give us the equation for the volume of the box as a function of x.