Question

An open box is to be made from a flat piece of material 14 inches long and 6 inches wide by cutting equal squares of length xfrom the corners and folding up the sides. Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors.

Answer 1

`f(x)=x(14-2x)(6-2x)`

Explanation:

We are given that

Length of flat piece of material=14 in

Width of flat piece of material=6 in

We have to find the volume of box as a function of x.

An open box is made from flat piece of material by cutting equal squares of length x from the corner and folding up the sides.

Therefore, Height of box=x in

Length of box=14-2x in

Width of box=6-2x in

We know that volume of box=
`length* breadth* height`

Using the formula

Volume of box=f(x)=
`x(14-2x)(6-2x)`