AP BIOLOGY

Detailed explanation-1: -Dimension. For a given shape, SA:V is inversely proportional to size. A cube 2 cm on a side has a ratio of 3 cm−1, half that of a cube 1 cm on a side. Conversely, preserving SA:V as size increases requires changing to a less compact shape.

Detailed explanation-2: -For a cube of size 3: The surface area is 54 (6 sides, each 3x3). The volume is 27 (3x3x3). So the surface area:volume ratio is 2.

Detailed explanation-3: -For a cube, the equation for surface area is S=6*L*L, where L is the length of a side. Similarly, the volume of a cube is V =L*L*L. So for a cube, the ratio of surface area to volume is given by the ratio of these equations: S/V = 6/L.