A bigger cell of the same shape has less surface per volume
- The idea
- Predict
- See it
- Why
- Check
The idea
“If a cell keeps its shape, its surface area to volume ratio stays the same as it grows or shrinks.”
Surface area and volume both go up as a cell grows, so their ratio seems like it should hold. They don't go up at the same rate.
The short version
The mistake: If a cell keeps its shape, its surface area to volume ratio stays the same as it grows or shrinks.
What's actually true: Volume grows faster than surface area, so the same shape at a larger size has a lower surface area to volume ratio.
- Surface area depends on length squared, and volume on length cubed. Double every dimension of a cell and its surface area goes up 4 times, but its volume goes up 8 times.
- So the ratio falls as a cell grows. For a cube it's 6 divided by the side, and for a sphere it's 3 divided by the radius. Shape only sets the top number.
- Materials enter and leave through the plasma membrane. A low ratio leaves less membrane to supply each bit of cytoplasm, which is one reason most cells stay small.
On the exam: Same shape at a bigger size means a lower surface area to volume ratio.