Which is the side length of a cube with a surface-area-to-volume ratio of 1/2?
Let the side length be represented by x. The faces of a cube are squares, so each face has an area of x^2. Since there are six faces total, the surface area is 6x^2. The volume is the side length cubed, or x^3. The surface area to volume ratio in terms of x is (6x^2)/(x^3), or 6/x. Setting this equals to 1/2 give x = 12. Thus, the side length is 12 units.