Surface Area to Volume Ratio and Exchange Surfaces
Work out surface area to volume ratios for cubes and simple shapes and show that the ratio falls as size rises. That falling ratio is why a large organism needs lungs, gills or a folded gut lining.
What a learner can do afterwards
- Calculates the surface area to volume ratio for cubes of different side length and states the trend.
- Names the features an effective exchange surface has and says what each one does to the rate.
- Uses the ratio to argue why a single-celled organism manages with no lungs at all.
1 · Read
Find the ratio in three steps. Work out surface area, work out volume, then divide area by volume. A 1 cm cube has six faces of 1, so 6, and a volume of 1, so the ratio is 6.
Grow the cube to 6 cm and the numbers change. Six faces of 36 give 216, and the volume is 216, so the ratio is 1. The ratio falls as the cube grows, because volume grows faster than area. That is part of why a bigger animal needs lungs or gills while the smallest creatures do not.
That falling ratio decides how animals breathe. A single cell swaps gases straight through its membrane and needs no lungs. A large animal cannot, so it uses lungs, gills, or a folded gut lining to gain area.
Good exchange surfaces share the same tricks: a huge area, a thin barrier, a rich blood supply to carry things away, and a moist lining to dissolve gases. Name each feature and say what it does to the rate.
Volume outgrows area as size rises, so big bodies need folded exchange surfaces.
2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.