Question

An open rectangular box is to be constructed by cutting square corners out if an 8- by 8- inch piece of cardbord and folding up the flaps

Answer 1

To construct an open rectangular box, cut square corners out of the cardboard and fold up the flaps. The volume of the box can be calculated by multiplying the length, width, and height. For example, if 2 inches are cut out from each corner, the volume of the box will be 32 cubic inches.

Step-by-step explanation:

To construct an open rectangular box, we need to cut square corners out of an 8-by-8-inch piece of cardboard and fold up the flaps. The dimensions of the box will be determined by the size of the square corners that are cut out. Let's say we cut out x inches from each corner. Then, the length of the box will be 8 - 2x inches and the width will be 8 - 2x inches. The height of the box will be x inches. So, the volume of the box can be calculated by multiplying the length, width, and height: (8 - 2x)(8 - 2x)(x) cubic inches.

For example, if we cut out 2 inches from each corner, then the dimensions of the box will be 8 - 2(2) = 4 inches by 8 - 2(2) = 4 inches by 2 inches. The volume of the box will be (4)(4)(2) = 32 cubic inches.