A manufacturer wants to package samples of a product in a box with a square base. the package is to have a volume of 100 cubic centimeters. what is the func that will describe the surface area of the box S(x) in ters of the length of a side of the base, X?

MY Solution: S(x)= 2X^2 + 400/X
is this correct

that's what I get, too

To find the surface area of the box with a square base, you need to determine the areas of all six sides of the box. Since the base is square, all four sides of the base have the same area, and the top and bottom of the box each have an area equal to the area of the base.

Let's denote the length of a side of the base as x. The area of each side of the base is simply x^2, and since there are four sides, the total area of the base is 4x^2.

To find the areas of the top and bottom of the box, we need to consider the volume of the box. The volume is given as 100 cubic centimeters, and since the base is square, we can write the volume equation as:

x^2 * h = 100

where h represents the height of the box. Solving for h gives us:

h = 100 / x^2

Since the top and bottom of the box each have a surface area of x^2, the total area for both is 2x^2.

Now, we can calculate the surface area of the four sides, which are the lateral faces. These are rectangles with dimensions x and h. Using the formula for the area of a rectangle, we have:

2(xh) = 2(x * (100 / x^2))
= 200 / x

Adding the base area, the top and bottom area, and the lateral area gives us the total surface area equation:

S(x) = 4x^2 + 2x^2 + 200 / x
= 6x^2 + 200 / x

So, the correct function that will describe the surface area of the box S(x) in terms of the length of a side of the base x is:

S(x) = 6x^2 + 200 / x

Therefore, your initial solution, S(x) = 2x^2 + 400 / x, is not correct.