Each of these three groups of cubes has an equal volume. However, their surface areas are vastly different. On the left, the single cube has a length, width, and height of 4 units, giving it a surface area of 6(4×4)=48 and a volume of 4^3=64. The middle eight cubes have a length, width, and height of 2, meaning a surface area of 8(6(2×2))=8×24=96. They also have a volume of 8(2^3)=8×8=64. The 64 cubes on the right have a length, width, and height of 1, leading to a surface area of 64(6(1×1))=64×6=384. The volume remains unchanged, because 64(1^3)=64×1=64. The surface area to volume ratio (SA:V), which is related to the amount of material available for reactions, changes for each as well. On the left, it is 48/64=0.75 or 3:4. The center has a SA/V of 96/64=1.5, or 3:2. On the right, the SA:V is 384/64=6, or 6:1.
Image by Matt Affolter.