AP BiologyUnit 2: Cells2.2
AP Biology · Unit 2 · Topic 2.2

Cell Size

Play it as a 3-minute lesson → short cards, one idea at a time

The lesson3 min read

Surface feeds, volume eats. Double the width: four times the surface, eight times the volume.

A cell's membrane has to supply its whole interior, and as a cell grows, its volume outruns its surface. That squeeze is why cells stay small, fold their membranes, or flatten out.

Key terms

  • Surface area — the size of the cell's outer boundary. Every nutrient coming in and every waste going out crosses it.
  • Volume — how much cytoplasm the cell holds. It sets demand: more cytoplasm uses more nutrients and makes more waste.
  • Surface area-to-volume ratio (SA:V) — surface area divided by volume. It tells you how much membrane serves each unit of cytoplasm.
  • Diffusion — molecules spreading from high to low concentration. Quick over a few micrometers, slow over millimeters.
  • Microvilli — finger-like projections of the membrane on cells lining the small intestine. They add surface with little added volume.

How it works

  1. Demand scales with volume. Every bit of cytoplasm uses nutrients and makes waste.
  2. Supply scales with surface area. Everything enters and leaves across the membrane.
  3. Grow a cube from edge s to 2s: surface area goes up 4 times (6s² → 24s²), volume 8 times (s³ → 8s³). SA:V halves.
  4. For a cube, SA:V = 6s² ÷ s³ = 6/s. For a sphere, it's 3/r. Either way, bigger means a lower ratio.
  5. Distance adds a second penalty. Diffusion time grows with the square of distance: twice as far to the center takes about four times as long.
  6. Past a certain size, the membrane can't serve the interior fast enough. Cells stay under that limit by dividing, or push past it by flattening or folding.

Why it matters

Expect a calculation: find SA:V for a cube or sphere, then compare. Biology buys extra surface all over: microvilli in the gut, root hairs, the alveoli in your lungs, cristae in mitochondria, the flattened disc of a red blood cell. The same math explains heat. A mouse has far more surface per gram than an elephant, so it loses heat faster for its size and must burn fuel faster, per gram, to stay warm.

Exam traps

TrapActually
Bigger cells have less surface area.Total surface area rises as a cell grows. What falls is surface per unit of volume, the ratio.
The cell with the most total membrane supplies its cytoplasm best.Divide by volume first. A small, folded cell can beat a larger cell that has more total membrane.
A rounder cell exchanges faster.A sphere has the least surface for its volume. Flattening or folding raises SA:V without adding cytoplasm.
Double the width, double the time for diffusion to reach the center.Diffusion time scales with distance squared. Double the width and the center waits about four times as long.
Worked example

A spherical cell with a 20 µm radius divides into eight equal daughter cells, each with a 10 µm radius. Total cytoplasm is unchanged. By what factor does total membrane area change, and what happens to SA:V? (Sphere: SA = 4πr², V = 4/3 πr³.)

  1. Check volume first: 8 × 4/3 π(10)³ = 4/3 π(8,000) = 4/3 π(20)³. Same cytoplasm, same demand.
  2. Parent surface: 4π(20)² = 1,600π µm². Daughters: 8 × 4π(10)² = 3,200π µm². Total membrane doubles.
  3. For a sphere, SA:V = 3/r, so the ratio goes from 3/20 = 0.15 µm⁻¹ to 3/10 = 0.30 µm⁻¹.

Total membrane area doubles, and SA:V doubles from 0.15 to 0.30 µm⁻¹, with the same total volume.

Halving the radius doubles SA:V, because a sphere's SA:V is 3/r. The near-miss is 'eight cells, so eight times the membrane.' Each daughter has only a quarter of the parent's surface, so the total is 8 × ¼ = 2 times.

Now try it on real exam-style questions

Ten questions on Cell Size, each with a ten-second explanation. Free, no account.

Three questions to check yourself

Question 1 · 2.2 Cell Size

In the human small intestine, which folds of the lining greatly increase the surface area for absorption?

  1. A Alveoli
  2. B Cilia
  3. C Flagella
  4. D Villi
Show the answer

D — Villi are folds of the small intestine lining that multiply the surface available for absorbing digested nutrients. Alveoli also increase surface area, but they are the tiny air sacs of the lungs used for gas exchange.

Question 2 · 2.2 Cell Size

Why does oxygen take longer to reach the center of a large cell than the center of a small cell?

  1. A Its plasma membrane is much thicker
  2. B It takes in less oxygen in total
  3. C The oxygen must diffuse a greater distance
  4. D Oxygen molecules move more slowly in large cells
Show the answer

C — Diffusion is fast over short distances but slow over long ones, and the center of a large cell lies farther from the membrane. A large cell actually takes in more oxygen in total; the problem is that each unit of its volume gets less, and the interior is harder to reach.

Question 3 · 2.2 Cell Size

For a fixed volume, which shape has the smallest surface area?

  1. A A cube
  2. B A sphere
  3. C A flat disk
  4. D A thin rod
Show the answer

B — A sphere encloses a given volume with the least possible surface, so round cells have the lowest surface area-to-volume ratio for their size. A cube looks compact, but its corners and edges add surface that a sphere avoids.