Question

An artist cuts 4 squares with side length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She bends up the sides and

welds the comers to form a rectangular garden fountain that is x ft high. Write and simplify a function for the volume of the fountain in terms
of x.
V(x) =
x+
x+

Answer 1

`V=4x^3-60x^2+216x`

Explanation:

Volume And Function s

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`

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)`

Operating and simplifying

`V=4x^3-60x^2+216x`