The volume of any prism is equal to the area of the base times its vertical height. Since the area of the rectangular prism is a square, the volume is expressed as:
V = s²h
The surface area is equal to the total areas of the faces of the planes. This includes the two bases on top and on the bottom, and the 4 rectangular lateral faces. The rectangular lateral face has an area of its length equal to height h multiplied with the width equal to the side of the square base. So, the surface area is expressed as:
SA = 2s² + 4sh
The first time is twice the area of the base, and the second term is four times the area of the lateral face. So, we want to express the surface area only in terms of s. Therefore, let's substitute an expression in terms of s to the h term above. Let's use the given volume equal to 2 cm³.
V = s²h = 2
Express in terms of s:
h = 2/s²
Then, let's substitute this to the equation for SA:
SA = 2s² + 4s(2/s²)
SA = 2s² + 8/s
