The first question is: A box with an open top isgoing to be constructed from a rectangular piece of cardboard. The cardboard measures 10 x 18 inches.

Question

The box is formed by cutting equal sized squares of side x, from the corners of the cardboard, then folding the sides up. What is the domain of the function v(x) that gives the volume of the box?

Answer 1

v(x) = (length)(width)(height)

v(x) = (18-2x)(10-2x)x. where 0 < x < 5

Note: 5 is half of the width of the piece of cardboard. Cutting 5" cuts the sheet of cardboard into 2 pieces.