Question

Let x represent the length of the side of a square, and also the edge of a cube. The area of the square is represented by f(x) = x^2. The surface area of the cube is represented by g(x) = 6x^2. Which statement describes g(x) in terms of f(x)?

Answer 1

g(x) describes the surface area of a cube and is equal to 6 times f(x), the area of one of the cube's faces (a square).

Step-by-step explanation:

The statement that describes g(x) in terms of f(x) is that the surface area of the cube is six times the area of the square. Given that f(x) represents the area of the square and f(x) = x^2, and g(x) represents the surface area of the cube and g(x) = 6x^2, it is clear that g(x) is equivalent to 6 times f(x).

By understanding that the cube is made up of six identical squares, we can deduce that the surface area of the cube is simply six times the area of one of its faces. Therefore, if f(x) is the area of one face (a square), then g(x), the total surface area, will be six times that amount. This is a straightforward example of dimensional analysis, utilizing the formula for the area of a square and extending it to find the surface area of a cube.