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### Course: AP®︎/College Biology>Unit 2

Lesson 2: Cell size

# Surface area to volume ratio of cells

In order to stay alive, cells exchange resources, waste, and energy with their environments. This exchange happens across the cell membrane. As the volume of a cell increases, the ratio of surface area to volume decreases, making these exchanges less efficient. Some cells have folds in their membranes, which increase their surface area to volume ratio.

## Want to join the conversation?

• i don't understand
how is it done the video helped only a bit still don't get
• Basically, cells have a limit as to how large they can get. Every cell has a limit of surface area to volume ratio to ensure that the exchange of resources and waste occurs quickly enough for the cell to survive. If cells were too big, diffusion would take an extremely long time, and a cell could die from starvation or poison itself with its wastes.
• it's stated that the less surface area per unit of volume, the harder it is for these transfers to occur. Why is that? What does surface area have to do with how much energy it takes for these transfers to occur?
• Hi there Savannah. Thank you for your question.

As a cell grows in size, the surface area gets bigger, but the volume gets bigger faster.

Thinking about this as a ratio (division), the volume is the denominator and the surface area is the numerator. If the volume is getting very big, then the ratio itself will be getting very small.

What this translates to is as a cell gets larger, with a larger volume, it has a smaller SA:V. A smaller SA:V means that diffusion of nutrients and diffusion of waste in less efficient (harder to do).

The rate of diffusion doesn't change, but it would take longer for the nutrients to diffuse through to the centre of the cell than a cell with a higher SA:V (a smaller cell - i.e. a cell with a smaller volume)
• If cells need to increase their surface area by folding their shape when they get too big, why are egg cells so huge, but in a spherical shape?
• Is there any video on Khan Academy regarding cell shape, to be specific, spherical cell shape and information about it?
• There are a few videos/articles that I know of: 1. Cell size,
2. 1 video and 1 article on the cytoskeleton, 3. The scale of cells.
• Can somebody please explain the equations in red and white, separately.
Thanks.
• Both equations are the ratio of the solid’s surface area to its volume. The red one is for a sphere, and the white one is for a cube.
• where is he getting his numbers?
• He is using the formula for the surface area of a sphere, and the formula for the volume of a sphere.

He then relates 'r' and talks about as the value of 'r' increases, the surface area to volume ratio decreases. (which makes diffusion of nutrients and waste products less efficient)
• how does increasing the surface area will increase the SA:V in the formula? isn't it always 3/r? how to show that SA:V increases in the formula?
• 1. SA increases by the 2nd power. V increases by 3rd power
2. yes
3. You can use Sal's formula
• I still don't get the question I'm trying to answer: will a highly flattened cell or a spherical cell achieve the largest volume?
• A really flat cell isn't going to have a lot of volume (because it's flat). Because there's so little volume, there's more surface area per unit of volume of a cell.

But with a spherical cell, there's a lot more volume, so there's less surface area to go around for each unit of volume.

So in general, a spherical cell will have a larger volume than a flat cell (if they're on a similar scale), but there's a limit to how big a spherical cell can get before it becomes too big.