Pre-calculus box problem?

Question

Find the volume of a rectangular box when the perimeter of its girth(cross section) is 108. Show the volume equation as a function of x.

Please explain the process, if possible! Thanks.

Answer 1

I'm guessing you mean a horizontal cross section. In this case, the width of the box could be called x and the height of the box, h.

Then,

V = h* x *(108-2x)/2

The explanation is that if the width of the box is x, then the perimeter minus 2x will be twice the width, since the perimiter is 2L+2W. Therefore, the width is half of (108-2x).

The volume of a rectangular prism is l*w*h

Answer 2

The volume is 108x where x is the length of the box.The volume of a box is length X width X height.

The cross section is width X height = 108.
So volume = 108x, where x is length.