Final answer:
The surface area of an open rectangular box with a square base can be expressed as a function of the length of one of the sides of the base. The volume of the box is used to find the height of the box, which is then used to calculate the surface area.
Step-by-step explanation:
The surface area of an open rectangular box with a square base can be expressed as a function of the length of one of the sides of the base.
Let's assume the length of one side of the base is 's'.
The volume of the box is given as 6 cubic meters. Since the base is square, the area of the base is s^2.
The height of the box can be found by dividing the volume by the base area: h = 6/s^2.
The surface area of the box can be calculated by adding the area of the base (s^2) and the areas of the four sides (4sh): SA = s^2 + 4sh = s^2 + 4s*(6/s^2).