Cell Theory: Prokaryotic & Eukaryotic Cells
Learn the three tenets of cell theory and who discovered them, compare prokaryotic vs eukaryotic and plant vs animal cells, and calculate surface-area-to-volume ratios.
What you'll do in this lesson
A voice-first session with the Crimsora tutor on Cell Theory: Prokaryotic & Eukaryotic Cells, then targeted practice and FRQs — with the tutor adapting to where you get stuck.
What this lesson covers
Before microscopes, nobody knew living things were built out of anything smaller than what the eye could see. Then people started grinding lenses, pointing them at cork, pond water, and their own scrapings of tooth plaque, and a whole hidden level of biology opened up. Out of about 175 years of that looking came cell theory: three short statements that quietly organize everything else you will study this year.
In this lesson you will state those three tenets and connect each one to the observations that produced it. Then you will sort cells into the two great structural camps — prokaryotic and eukaryotic — and separate plant from animal cells by which structures each one carries. Finally you will do the math that explains a fact you might otherwise take for granted: cells are almost all microscopically small, and geometry, not chance, is the reason why.
In this lesson you will state those three tenets and connect each one to the observations that produced it. Then you will sort cells into the two great structural camps — prokaryotic and eukaryotic — and separate plant from animal cells by which structures each one carries. Finally you will do the math that explains a fact you might otherwise take for granted: cells are almost all microscopically small, and geometry, not chance, is the reason why.
The Three Tenets of Cell Theory and the Observations Behind Them
Cell theory says three things:
First, all living things are made of one or more cells. Second, the cell is the basic unit of structure and function in living things. Third, all cells come from pre-existing cells.
Each tenet came from somebody's microscope. In 1665 Robert Hooke sliced thin cork and saw tiny empty boxes that reminded him of the small rooms monks lived in, so he called them cells. He was looking at dead plant cell walls, not living cells. Around the same time Anton van Leeuwenhoek, using better single-lens microscopes, saw moving single-celled organisms in pond water and bacteria in scrapings from his teeth — evidence that cells could be whole living things.
More than 150 years later, the botanist Matthias Schleiden concluded that all plant tissue is made of cells, and the zoologist Theodor Schwann concluded the same for animal tissue. Together those two observations give tenet one and support tenet two. Tenet three took longest. Many scientists still believed in spontaneous generation — that life could arise from non-living material. Rudolf Virchow stated in 1855 that every cell arises from another cell, and Louis Pasteur's swan-neck flask experiments showed that sterilized broth stayed sterile unless microbes from the air could reach it.
A common mistake on homework is crediting Hooke with cell theory. Hooke named cells; he did not claim all organisms are made of them. Another frequent error is stating tenet two as "cells are the smallest thing alive." The claim is about structure and function: whatever an organism does — metabolism, growth, response — happens because of what its cells do. Viruses, which are not cells and cannot reproduce without a host, are the classic borderline case students raise, and they are usually treated as not alive precisely because they violate cell theory.
First, all living things are made of one or more cells. Second, the cell is the basic unit of structure and function in living things. Third, all cells come from pre-existing cells.
Each tenet came from somebody's microscope. In 1665 Robert Hooke sliced thin cork and saw tiny empty boxes that reminded him of the small rooms monks lived in, so he called them cells. He was looking at dead plant cell walls, not living cells. Around the same time Anton van Leeuwenhoek, using better single-lens microscopes, saw moving single-celled organisms in pond water and bacteria in scrapings from his teeth — evidence that cells could be whole living things.
More than 150 years later, the botanist Matthias Schleiden concluded that all plant tissue is made of cells, and the zoologist Theodor Schwann concluded the same for animal tissue. Together those two observations give tenet one and support tenet two. Tenet three took longest. Many scientists still believed in spontaneous generation — that life could arise from non-living material. Rudolf Virchow stated in 1855 that every cell arises from another cell, and Louis Pasteur's swan-neck flask experiments showed that sterilized broth stayed sterile unless microbes from the air could reach it.
A common mistake on homework is crediting Hooke with cell theory. Hooke named cells; he did not claim all organisms are made of them. Another frequent error is stating tenet two as "cells are the smallest thing alive." The claim is about structure and function: whatever an organism does — metabolism, growth, response — happens because of what its cells do. Viruses, which are not cells and cannot reproduce without a host, are the classic borderline case students raise, and they are usually treated as not alive precisely because they violate cell theory.
Prokaryotic and Eukaryotic Cells
All cells share four features: a plasma membrane, cytoplasm, ribosomes, and DNA. The split between prokaryotes and eukaryotes is about how that DNA is housed and how much internal compartmentalization exists.
Prokaryotic means "before nucleus." In a prokaryote — all bacteria and all archaea — the DNA sits in a region of cytoplasm called the nucleoid with no membrane around it, and the chromosome is usually a single circular loop. There are no membrane-bound organelles at all: no mitochondria, no endoplasmic reticulum, no Golgi. Ribosomes are present but are smaller than eukaryotic ones. Nearly all prokaryotes have a cell wall, many have a capsule outside it, and many have flagella or pili.
Eukaryotic cells — protists, fungi, plants, animals — enclose linear chromosomes inside a true nucleus bounded by a double membrane, and they carry many membrane-bound organelles. They are also much bigger, typically 10 to 100 micrometers across versus roughly 1 to 5 micrometers for a bacterium.
Two misconceptions to kill now. Prokaryotes are not "simple" — they are metabolically the most versatile cells on Earth. And "no organelles" is sloppy: prokaryotes have ribosomes, which are organelles in the broad sense. The accurate statement is that they lack membrane-bound organelles, so write it that way.
Prokaryotic means "before nucleus." In a prokaryote — all bacteria and all archaea — the DNA sits in a region of cytoplasm called the nucleoid with no membrane around it, and the chromosome is usually a single circular loop. There are no membrane-bound organelles at all: no mitochondria, no endoplasmic reticulum, no Golgi. Ribosomes are present but are smaller than eukaryotic ones. Nearly all prokaryotes have a cell wall, many have a capsule outside it, and many have flagella or pili.
Eukaryotic cells — protists, fungi, plants, animals — enclose linear chromosomes inside a true nucleus bounded by a double membrane, and they carry many membrane-bound organelles. They are also much bigger, typically 10 to 100 micrometers across versus roughly 1 to 5 micrometers for a bacterium.
| Feature | Prokaryotic | Eukaryotic |
|---|---|---|
| Nucleus | absent (nucleoid) | present |
| DNA shape | circular | linear chromosomes |
| Membrane-bound organelles | none | many |
| Ribosomes | present, smaller | present, larger |
| Typical diameter | 1–5 micrometers | 10–100 micrometers |
| Cell wall | almost always | plants, fungi and many protists; never animals |
| Organisms | bacteria, archaea | protists, fungi, plants, animals |
Plant Cells and Animal Cells
Both are eukaryotic, so both have a nucleus, mitochondria, endoplasmic reticulum, Golgi, and ribosomes. The differences are a short list, and questions in this unit almost always come down to that list.
Plant cells have a rigid cell wall made of cellulose outside the plasma membrane, chloroplasts for photosynthesis, and usually one large central vacuole that stores water and pushes outward on the wall to create turgor pressure. Plant cells lack centrioles in most species.
Animal cells have no cell wall, no chloroplasts, and typically several small vacuoles rather than one big one. They have centrioles that organize the spindle during cell division, and lysosomes are prominent.
Where students go wrong: they say plants do not have mitochondria because they photosynthesize. Plants absolutely have mitochondria — photosynthesis makes glucose, and cellular respiration in mitochondria is still what turns glucose into usable ATP. Leaf cells run both processes.
A second trap is treating cell wall and cell membrane as synonyms. Every cell has a plasma membrane; only some have a wall, and the wall lies outside the membrane. A third is assuming any cell with a wall is a plant cell. Fungi have walls of chitin, and bacteria have walls of peptidoglycan, so "has a wall" alone is not enough to identify a plant. Look for chloroplasts plus a nucleus if you want to be sure.
Plant cells have a rigid cell wall made of cellulose outside the plasma membrane, chloroplasts for photosynthesis, and usually one large central vacuole that stores water and pushes outward on the wall to create turgor pressure. Plant cells lack centrioles in most species.
Animal cells have no cell wall, no chloroplasts, and typically several small vacuoles rather than one big one. They have centrioles that organize the spindle during cell division, and lysosomes are prominent.
| Structure | Plant | Animal |
|---|---|---|
| Cell wall (cellulose) | yes | no |
| Chloroplasts | yes | no |
| Large central vacuole | yes | no |
| Centrioles | usually no | yes |
| Shape | fixed, boxy | flexible, varied |
A second trap is treating cell wall and cell membrane as synonyms. Every cell has a plasma membrane; only some have a wall, and the wall lies outside the membrane. A third is assuming any cell with a wall is a plant cell. Fungi have walls of chitin, and bacteria have walls of peptidoglycan, so "has a wall" alone is not enough to identify a plant. Look for chloroplasts plus a nucleus if you want to be sure.
Why Surface-Area-to-Volume Ratio Keeps Cells Small
Everything a cell needs — oxygen, glucose, ions — enters through its surface, and every waste product leaves the same way. The demand for those materials, however, depends on how much living cytoplasm there is, which is volume. So the useful quantity is the ratioFor a cube of side length , surface area is and volume is , soThe ratio is inversely proportional to size. Double the side length and the ratio is cut in half. For a sphere of radius the same pattern appears: .
Here is the consequence. When a cell grows, volume grows with the cube of length while surface area grows only with the square. Past a certain size the membrane cannot import nutrients or dump wastes fast enough for the interior, and diffusion — which is slow over long distances — cannot move molecules to the center quickly enough. The cell either divides or dies. That is why cells stay microscopic instead of growing into one giant blob.
Cells that need extra exchange capacity cheat with shape rather than size. Root hair cells and the microvilli of intestinal cells are thin projections that add surface area without adding much volume. Flattened cells and long thin nerve axons do the same. Notice the general rule: for fixed volume, the flatter or more folded the shape, the higher the ratio.
The most common error here is reporting a bigger surface area as "better exchange" without dividing by volume. A whale has more surface area than a bacterium; the bacterium has the vastly better ratio, and the ratio is what determines whether the interior can be supplied.
Here is the consequence. When a cell grows, volume grows with the cube of length while surface area grows only with the square. Past a certain size the membrane cannot import nutrients or dump wastes fast enough for the interior, and diffusion — which is slow over long distances — cannot move molecules to the center quickly enough. The cell either divides or dies. That is why cells stay microscopic instead of growing into one giant blob.
Cells that need extra exchange capacity cheat with shape rather than size. Root hair cells and the microvilli of intestinal cells are thin projections that add surface area without adding much volume. Flattened cells and long thin nerve axons do the same. Notice the general rule: for fixed volume, the flatter or more folded the shape, the higher the ratio.
The most common error here is reporting a bigger surface area as "better exchange" without dividing by volume. A whale has more surface area than a bacterium; the bacterium has the vastly better ratio, and the ratio is what determines whether the interior can be supplied.
Putting the Ideas Together
These three threads are not separate facts; they interlock. Cell theory's third tenet — cells come from cells — is the only reason surface-area-to-volume constraints matter biologically. A cell that outgrows its ratio does not just shrink back; it divides, producing two smaller cells that each restore a workable ratio. Growth in multicellular organisms therefore means making more cells, not bigger ones. Your muscle cells are not larger than a mouse's; you simply have more of them.
Compartmentalization is the other half of the answer. Eukaryotic cells got around some of the size limit by building internal membranes. Membrane-bound organelles add enormous internal surface area — the folded inner membrane of a mitochondrion, the stacked sheets of rough endoplasmic reticulum — so exchange surfaces exist throughout the interior instead of only at the outer boundary. That is a structural reason eukaryotes can be ten to a hundred times wider than prokaryotes while still functioning. You will see each of those organelles in detail in the next lesson.
When you are asked to identify a mystery cell, work through a short decision path. Is there a nucleus? No means prokaryote, and you are done. Yes means eukaryote, so check next for chloroplasts and a large central vacuole; both present with a cellulose wall points to a plant cell. No wall, no chloroplasts, centrioles present points to an animal cell. A wall and a nucleus but no chloroplasts and no central vacuole points to a fungal cell. Naming the structure that decides the case is what makes an answer complete — "it has a nucleus, so it is eukaryotic" is an answer, while "it looks complicated" is not.
Compartmentalization is the other half of the answer. Eukaryotic cells got around some of the size limit by building internal membranes. Membrane-bound organelles add enormous internal surface area — the folded inner membrane of a mitochondrion, the stacked sheets of rough endoplasmic reticulum — so exchange surfaces exist throughout the interior instead of only at the outer boundary. That is a structural reason eukaryotes can be ten to a hundred times wider than prokaryotes while still functioning. You will see each of those organelles in detail in the next lesson.
When you are asked to identify a mystery cell, work through a short decision path. Is there a nucleus? No means prokaryote, and you are done. Yes means eukaryote, so check next for chloroplasts and a large central vacuole; both present with a cellulose wall points to a plant cell. No wall, no chloroplasts, centrioles present points to an animal cell. A wall and a nucleus but no chloroplasts and no central vacuole points to a fungal cell. Naming the structure that decides the case is what makes an answer complete — "it has a nucleus, so it is eukaryotic" is an answer, while "it looks complicated" is not.
Key terms
- Cell theory.
- The unifying principle that all living things are made of cells, that the cell is the basic unit of structure and function, and that all cells arise from pre-existing cells.
- Prokaryotic cell.
- A cell whose DNA is not enclosed in a nucleus and which has no membrane-bound organelles; includes all bacteria and archaea.
- Eukaryotic cell.
- A cell with a true membrane-bound nucleus containing linear chromosomes, plus membrane-bound organelles; includes protists, fungi, plants, and animals.
- Nucleoid.
- The region of a prokaryotic cell's cytoplasm where the circular chromosome is concentrated, with no surrounding membrane.
- Surface-area-to-volume ratio.
- Surface area divided by volume; for a cube of side it equals , so the ratio falls as a cell gets larger, limiting how big a cell can grow.
- Spontaneous generation.
- The discarded idea that living organisms can arise from non-living matter; its refutation by Pasteur supported the third tenet of cell theory.
- Central vacuole.
- A single large fluid-filled organelle in most mature plant cells that stores water and solutes and generates turgor pressure against the cell wall.
- Turgor pressure.
- The outward pressure of water inside a plant cell pushing against the cell wall, which keeps non-woody plant tissue firm.
Worked example
Two model cells are cubes. Cell A has a side length of 2 micrometers; Cell B has a side length of 6 micrometers. Calculate the surface area, volume, and surface-area-to-volume ratio of each, and explain which cell can supply its interior more effectively.
Start with the formulas for a cube of side : surface area and volume .
Cell A, with : surface area square micrometers, and volume cubic micrometers. So , or .
Cell B, with : surface area square micrometers, and volume cubic micrometers. So , or .
Check against the shortcut . For Cell A, . For Cell B, . Both match.
Interpret the numbers. Cell B has nine times the surface area of Cell A, so a careless answer picks B. But B has twenty-seven times the volume — three times the linear size means times the area and times the volume. Each cubic micrometer of cytoplasm in Cell A is served by 3 square micrometers of membrane, while each cubic micrometer in Cell B is served by only 1.
Cell A therefore supplies its interior far more effectively: it has three times the membrane per unit of cytoplasm, and nutrients diffusing inward have to travel only 1 micrometer to reach the center instead of 3. This is why a growing cell divides rather than continuing to enlarge.
Cell A, with : surface area square micrometers, and volume cubic micrometers. So , or .
Cell B, with : surface area square micrometers, and volume cubic micrometers. So , or .
Check against the shortcut . For Cell A, . For Cell B, . Both match.
Interpret the numbers. Cell B has nine times the surface area of Cell A, so a careless answer picks B. But B has twenty-seven times the volume — three times the linear size means times the area and times the volume. Each cubic micrometer of cytoplasm in Cell A is served by 3 square micrometers of membrane, while each cubic micrometer in Cell B is served by only 1.
Cell A therefore supplies its interior far more effectively: it has three times the membrane per unit of cytoplasm, and nutrients diffusing inward have to travel only 1 micrometer to reach the center instead of 3. This is why a growing cell divides rather than continuing to enlarge.
Practice questions
Which observation most directly supports the third tenet of cell theory, that all cells come from pre-existing cells?
- Hooke's drawing of box-like compartments in a slice of cork
- Leeuwenhoek's discovery of swimming single-celled organisms in pond water
- Pasteur's finding that sterilized broth stayed free of microbes unless exposed to air
- Schleiden's conclusion that all plant tissues are composed of cells
Answer: Pasteur's finding that sterilized broth stayed free of microbes unless exposed to air
The third tenet is about the origin of cells, so the supporting evidence must rule out cells appearing from non-living material. Pasteur's flasks did exactly that: microbes grew only when pre-existing cells from the air could enter, refuting spontaneous generation. Hooke's cork showed that cells exist, Leeuwenhoek's pond water showed that cells can be whole organisms, and Schleiden's work supports the first tenet — none of the three addresses where a new cell comes from.
A student examines an unknown cell under a microscope and reports: no nucleus visible, a cell wall present, DNA in a single circular loop, ribosomes present, no mitochondria. Classify the cell as specifically as the evidence allows, name the two features that were most decisive, and explain why the absence of mitochondria is consistent with your classification.
Answer: It is a prokaryotic cell (a bacterium or archaean). The decisive features are the absence of a nucleus and the single circular chromosome. Prokaryotes have no membrane-bound organelles at all, so the missing mitochondria fit the classification rather than contradicting it.
Work the decision path in order. The absence of a nucleus rules out every eukaryote immediately, so plant, animal, and fungal cells are all out even though a wall is present. The circular chromosome confirms it, because eukaryotes package DNA as linear chromosomes. The wall alone is not diagnostic, since bacteria, fungi, and plants all have walls made of different materials. Mitochondria are membrane-bound organelles, and the defining structural feature of prokaryotes is that they lack membrane-bound organelles; the cell still makes ATP, just without a dedicated organelle. Ribosomes are present because every cell must build proteins, which is exactly why ribosomes are not useful for telling the two cell types apart.
Explain why intestinal cells are covered in thousands of tiny finger-like projections called microvilli, using the idea of surface-area-to-volume ratio.
Answer: Microvilli raise the cell's surface area without meaningfully increasing its volume, which raises the surface-area-to-volume ratio and lets the cell absorb far more nutrients per unit of cytoplasm than a smooth-surfaced cell of the same size could.
Absorption happens across membrane, so absorption capacity scales with surface area, while the cell's metabolic needs and internal transport distances scale with volume. A cell cannot solve an absorption problem by growing, because volume grows faster than area — for a cube, the ratio actually falls as increases. Changing shape is the alternative: thin projections are almost all membrane and very little interior, so area climbs steeply while volume barely moves. Root hair cells in plants and the folded inner membrane of a mitochondrion use the same geometric strategy.
FAQ
- What are the three parts of cell theory in the simplest wording?
- All living things are made of one or more cells; the cell is the basic unit of structure and function in living things; all cells come from pre-existing cells. If you need names attached, Schleiden and Schwann support the first two, and Virchow (with Pasteur's evidence) supports the third.
- Do viruses break cell theory?
- They sit outside it. A virus is not a cell — it has no plasma membrane enclosing cytoplasm, no ribosomes, and it cannot copy itself without hijacking a host cell's machinery. Because it fails the first and third tenets, most biologists classify viruses as non-living, which is why cell theory is stated as applying to living things.
- Are bacteria prokaryotic or eukaryotic, and what about fungi?
- All bacteria and all archaea are prokaryotic: no nucleus, no membrane-bound organelles, circular DNA. Fungi, including yeast and mushrooms, are eukaryotic — they have a true nucleus and organelles, plus a cell wall made of chitin rather than cellulose. A wall by itself never tells you the cell type.
- Why can't a cell just grow bigger instead of dividing?
- Volume increases with the cube of length while surface area increases only with the square, so the surface-area-to-volume ratio drops as a cell enlarges. Eventually the membrane cannot bring in nutrients and remove wastes fast enough for the larger interior, and diffusion to the center becomes too slow. Dividing produces two smaller cells that each have a healthy ratio again.
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