Answer:
![V=4x^3-60x^2+216x](https://tex.z-dn.net/?f=V%3D4x%5E3-60x%5E2%2B216x)
Step-by-step explanation:
<u>Volume And Function
s</u>
Geometry can usually be joined with algebra to express volumes as a function of some variable. The volume of a parallelepiped of dimensions a,b,c is
![V=abc](https://tex.z-dn.net/?f=V%3Dabc)
Our problem consists in computing the volume of a box made with some sheet of metal 12 ft by 18 ft. The four corners are cut by a square distance x as shown in the image below
.
If the four corners are to be lifted and a box formed, the base of the box will have dimensions (12-2x)(18-2x) and the height will be x. The volume of the box is
![V=x(12-2x)(18-2x)](https://tex.z-dn.net/?f=V%3Dx%2812-2x%29%2818-2x%29)
Operating and simplifying
![V=4x^3-60x^2+216x](https://tex.z-dn.net/?f=V%3D4x%5E3-60x%5E2%2B216x)