What is the volume of a box that can be created from a sheet of metal that measures 12 inches by 30 inches? Assume there is no top to the box.
If this is the typical question where equal sized squares are cut out at each corner, the volume will depend on the size of the cut-out squares
Suppose we cut out a square on each corner of x inches by x inches
then length of base = 30-2x
width of base = 12-2x
height = x
volume = x(30-2x)(12-2x) , where clearly 0<x<6
Perhaps, did the question ask for the maximum volume ?
I assume that square corners are cut and the sides are folded up, so that the sides are all the same height, call it z.
v = (12-2z)(30-2z)(z)
To find the volume of a box, we need to know the length, width, and height. In this case, we are given the dimensions of the sheet of metal, 12 inches by 30 inches.
To create a box, we can fold the sheet of metal into a rectangular shape, forming the bottom and four sides of the box. Since there is no top, the height of the box will be determined by the width of the sheet of metal.
In this case, the width of the sheet of metal is 30 inches. Thus, the height of the box will also be 30 inches.
So, the length, width, and height of the box are 12 inches, 30 inches, and 30 inches respectively.
To find the volume, we use the formula: Volume = length × width × height.
Plugging in the values, we get: Volume = 12 inches × 30 inches × 30 inches = 10,800 cubic inches.
Therefore, the volume of the box that can be created from the given sheet of metal is 10,800 cubic inches.