Question

Dena is going to construct a paper box. She will make the box x inches wide. The height of the box is 3 inches greater than the width, and the box is twice as deep as it is high. The volume of the box is 6464 in33. Which equation correctly describes the volume of the box?

Answer 1

`64=(2x+6)(x+3)(x)`

is the required equation for volume of box.

Explanation:

We are given the following in the question:

The box is
`x` inches wide.

Width, w =

`x\text{ inches}`

Height of box, h =

`(x+3)\text{ inches}`

Length of box, l =

`=2* \text{Height of box}\\=2* (x+3)\\=(2x+6)\text{ inches}`

Volume of box = 64 cubic inches

Formula:

`V = l* w* h`

Putting values, we get,

`V = (2x+6)(x+3)(x)\\64=(2x+6)(x+3)(x)\\64 = (2x+6)(x^2+3x)\\64 = 2x^3+6x^2+6x^2+18x)\\64 = 2x^3+12x^2+18x\\\Rightarrow 2x^3+12x^2+18x-64=0`

is the required equation.