Math Question

Question

You want to make an open box (it has no lid) with a square bottom, a height of 4 inches, and a volume of 256 cubic inches. To do this, you take a square piece of cardboard, cut 4-inch-long squares from each corner and fold up the edges. What should the dimensions of the cardboard be before you cut it? Suggestion: Refer to the figures below, where x is in inches. Remember that for a box,
Volume = Length × Width × Height.
Use the dimensions shown in the figure on the right to calculate the volume of the box in terms of x, and set that equal to 256 cubic inches.

Answer 1

Following instructions:

    Volume = Length × Width × Height

       256   =   x       *    x      *    4

 

Solve for x:

       256 = 4x²

        64 = x²

         x = 8 inches         [note:  (-8) doesn't make sense]

 

"What should the dimensions of the cardboard be before you cut it? "

      4 inches to fold up  + 8 inches for the base + 4 inches to fold up

      oh, it's a square, the other side is the same

 

The original cardboard should be 16 inches x 16 inches.

 

Note:  Visual learning is great!  If you don't have computer graphics, find some paper with lines, make lines in the other direction (now you have small squares), cut a 16x16 "original" piece, cut 4x4 from each corner, fold sides upward, then calculate the area based on the Length x Width x Height.