Question

An open box is to be made from a flat square piece of material 16 inches in length and width by cutting equal squares of length x x from the corners and folding up the sides. Write the volume V V of the box as a function of x x. Leave it as a product of factors; you do not have to multiply out the factors.

Answer 1

V = x(19-2x)(4-2x)

Explanation:

We are given;

Length of flat piece of material =19 inches

Width of flat piece = 4 inches

We are told that the open box is to be made from a flat piece by cutting equal squares of length x from the corners and folding up the sides

Thus, we will now have;

length of open box = (19-2x) inches

Width of open box = (4-2x) inches

Height of box = x inches

We know that: Volume of box = length × width × height

So, plugging in the relevant values, we have;

Volume of box(V) = x(19-2x)(4-2x)