Question

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 23 ft by 13 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way.

Answer 1

To find the volume of the largest box that can be formed, we need to determine the dimensions of the resulting piece of cardboard after removing squares from each corner. By taking the derivative of the volume function and solving for x, we can find the value that maximizes the volume. Substituting this value back into the volume function will give us the volume of the largest box that can be formed.

Step-by-step explanation:

The volume of the largest box that can be formed can be calculated by finding the dimensions of the resulting piece of folded cardboard. The dimensions of the cardboard after cutting out the squares from each corner are (23-2x) ft by (13-2x) ft by x ft. To find the value of x that maximizes the volume, we can take the derivative of the volume function, set it equal to zero, and solve for x. The volume of the largest box can then be calculated by substituting the value of x back into the volume function.