Question

An open box is to be made out of a 6-inch by 18 -inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box t"

Answer 1

The dimensions of the open box will be 18 - 2x inches in length, 6 - 2x inches in width, and x inches in height, where x is the size of the square cut-outs.

Step-by-step explanation:

To create an open box from a 6-inch by 18-inch piece of cardboard by cutting out equal-sized squares from the corners and folding up the sides, we need to define the size of the square cut-outs. Let's assume that the side of the square to be cut out is x inches. After cutting and folding, the length of the box will be 18 - 2x inches, the width will be 6 - 2x inches, and the height will be x inches.

The dimensions of the resulting box will depend on the value chosen for x. To maximize the volume of the box or to meet specific size requirements, we would need to determine the appropriate value for x, which might involve solving an equation or optimizing a function representing the volume of the box, V(x) = x(18 - 2x)(6 - 2x).