Question

an open box is made from a square piece of cardboard 28 inches on a side by cutting identical squares from the corners and turning up the sides. use this information to complete parts a through c. find and interpret v(6). select the correct choice below and, if necessary, fill in the answer box to complete your choice. (simplify your answer. type an integer or a decimal.) a. the volume of the box v(6) is cubic inches, when the side of the square cut from each corner of the piece of cardboard is 6 inches. b. the volume of the box v(6) is cubic inches, when the side of the square cut from the center of the piece of cardboard is 6 inches. c. the volume of the box v(6) is cubic inches, when the side of the square cut from the center of each edge of the piece of cardboard is 6 inches. d. the volume of the box v(6) is cubic inches, when the side of the square cut from each corner and the center of each edge of the piece of cardboard is 6 inches.

Explanation:

Step1: Determine box dimensions

If we cut a square of side - length $x = 6$ inches from each corner of a 28 - inch by 28 - inch square cardboard and fold up the sides, the length and width of the base of the box will be $l=w = 28 - 2x=28 - 2\times6=28 - 12 = 16$ inches, and the height of the box $h=x = 6$ inches.

Step2: Calculate the volume of the box

The volume formula for a rectangular - box is $V=l\times w\times h$. Substituting $l = 16$, $w = 16$, and $h = 6$ into the formula, we get $V=16\times16\times6=1536$ cubic inches. The volume $V(6)$ represents the volume of the box when the side - length of the square cut from each corner is 6 inches.

Answer:

A. The volume of the box V(6) is 1536 cubic inches, when the side of the square cut from each corner of the piece of cardboard is 6 inches.