Question

By cutting away an x-by- x square from each corner of a rectangular piece of cardboard and folding up the resulting flaps, a box with no top can be constructed. If the piece of cardboard is 52 inches long by 30 inches wide, find a function in the variable × giving the volume of the resulting box. Volume, as a function of x= Determine the domain of the function for volume.

Answer 1

The volume of the resulting box can be calculated using the formula (52-2x)(30-2x)(x).

Step-by-step explanation:

To find the volume of the resulting box, we need to determine the dimensions of the box after the corners have been cut and the flaps have been folded up. The original dimensions of the piece of cardboard are 52 inches long by 30 inches wide. By cutting a square with side length x from each corner, the new dimensions of the cardboard will be (52-2x) inches long and (30-2x) inches wide. The height of the box will be x inches. Therefore, the volume of the box is (52-2x)(30-2x)(x) cubic inches.