[[Cell Structure and Function]]

Surface area-to-volume ratio (SA:V) controls how well a cell exchanges materials and energy with its environment. Smaller cells have higher SA:V, so more efficient. As things get bigger, cells require more adaptations to remain fast.

# Summary
* Higher SA:V means more efficient exchange.
* Volume grows faster than SA as a cell gets bigger, so SA:V decreases.
* Folds and projections like microvilli and root hairs increase SA without adding much V.
* Lower SA:V in larger bodies slows heat exchange and is linked to lower metabolic rate.

Plasma membrane SA must be large enough to exchange stuff fast enough for cell needs. 
SA:V doesn't only affect size, but also shape. Sphere isn't all that efficient for SA:V. 

- _Sphere:_ SA = 4πr², V = (4/3)πr³
- _Cube:_ SA = 6s², V = s³
- _Cylinder:_ SA = 2πrh + 2πr², V = πr²h
- _Rectangular Solid:_ SA = 2(lw + lh + wh), V = lwh

Because SA:V impacts thermal energy transfer, larger organisms lose heat slower than smaller organisms proportionally.

| Term                         | Definition                                                                                                                                                         |
| ---------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
| heat exchange                | The transfer of thermal energy between an organism's body and the surrounding environment; rate decreases as organism size increases.                              |
| membrane folds               | Infoldings of the cell membrane that increase surface area to facilitate more efficient material exchange in complex cells.                                        |
| metabolic rate               | The rate at which an organism uses energy; typically higher per unit body mass in smaller organisms than in larger organisms.                                      |
| nutrient exchange            | The process by which cells obtain necessary nutrients from the environment.                                                                                        |
| plasma membrane              | The selectively permeable membrane that surrounds the cell, composed of phospholipids, proteins, and other molecules that regulate what enters and exits the cell. |
| surface area-to-volume ratio | The relationship between the total surface area and the total volume of a cell or organism; affects the efficiency of material exchange with the environment.      |
| thermal energy exchange      | The transfer of heat energy between an organism and its environment.                                                                                               |
| waste products               | Byproducts of cellular metabolism that must be eliminated from cells or organisms.                                                                                 |