AP Biology · Lesson 1

Organelles and cell size

Know Know it

Every cell has a plasma membrane, cytoplasm, DNA and ribosomes. Prokaryotic cells stop there: they have no nucleus and no organelles bound by membranes. Eukaryotic cells add a nucleus and a set of membrane-bound organelles, each with its own job.

Proteins for export or for membranes are made by ribosomes on the rough endoplasmic reticulum (rough ER). They enter the ER, are carried in vesicles to the Golgi complex to be modified and sorted, and then ride vesicles to the plasma membrane. Proteins that stay in the cytosol are made on free ribosomes. The smooth ER has no ribosomes; it makes lipids and helps break down some toxins.

Mitochondria make most of a eukaryotic cell's ATP; their folded inner membrane gives a large area for that work. Chloroplasts in plants and algae capture light energy to make sugar. Lysosomes hold digestive enzymes. A plant's large central vacuole stores water and helps keep the cell firm.

Cells exchange food, gases and wastes across their surface, but they use those materials throughout their volume. For a cube with side s, surface area is 6 x s x s and volume is s x s x s, so the surface-area-to-volume ratio is 6 divided by s. Doubling the side halves the ratio. That is why most cells are small, and why large cells are often long, thin, flat or folded.

Trap Bigger cell, more surface, smaller ratio

A larger cell has more surface area in total, but each unit of its volume gets less surface to serve it. Questions about exchange rates turn on the ratio, not on the total surface area.

Worked example Easy

A gland cell makes a protein and releases it outside the cell. In what order does the protein pass through these structures?

  1. Golgi complex, rough ER, vesicle, plasma membrane
  2. Rough ER, Golgi complex, vesicle, plasma membraneAnswer
  3. Smooth ER, lysosome, vesicle, plasma membrane
  4. Rough ER, mitochondrion, Golgi complex, nucleus

How to solve it

  1. A protein for export is made by ribosomes attached to the rough ER.
  2. Vesicles carry it to the Golgi complex for modifying and sorting.
  3. A new vesicle takes it to the plasma membrane, where it is released.

Why each choice is right or wrong

  • A. Incorrect. Starting at the Golgi complex reverses the first two steps; the protein is made at the rough ER first.
  • B. Correct. Ribosomes on the rough ER make the protein, the Golgi complex modifies and sorts it, and a vesicle carries it to the membrane.
  • C. Incorrect. The smooth ER has no ribosomes, and a lysosome digests material rather than shipping a protein out.
  • D. Incorrect. A mitochondrion makes ATP and the nucleus holds DNA; neither is a stop on the way out of the cell.

Explain Explain it

Task verbs: calculate, explain

For a size question, calculate first and then explain. Work out surface area and volume, divide, and compare the ratios. Then link the larger ratio to more membrane per unit of volume, so materials can enter and leave fast enough to meet the cell's needs.

Worked example Medium

A model cell is a cube 3 cm on each side. What is its surface-area-to-volume ratio?

  1. 1 to 2
  2. 3 to 1
  3. 2 to 1Answer
  4. 6 to 1

How to solve it

  1. Surface area: 6 faces x 3 cm x 3 cm = 54 square cm.
  2. Volume: 3 cm x 3 cm x 3 cm = 27 cubic cm.
  3. Ratio: 54 / 27 = 2, so 2 to 1. Check with the shortcut 6 / 3 = 2.

Why each choice is right or wrong

  • A. Incorrect. 1 to 2 flips the ratio, dividing volume by surface area instead of surface area by volume.
  • B. Incorrect. 3 to 1 is the ratio for a cube 2 cm on a side, which has 24 square cm over 8 cubic cm.
  • C. Correct. Surface area is 6 x 3 x 3 = 54 square cm and volume is 3 x 3 x 3 = 27 cubic cm, so 54 to 27 is 2 to 1.
  • D. Incorrect. 6 to 1 is the ratio for a cube 1 cm on a side, not for a cube 3 cm on a side.

Explain Your turn

Calculate the surface-area-to-volume ratio of a cube 1 cm on a side and of a cube 4 cm on a side, showing the surface area and volume of each. Then, using those two ratios, explain why a small cell can take in materials faster for its volume than a large cell.

Write it, then compare. Nothing you type here is saved or graded.

Compare with a model answer

A full answer does this

  • Gives 6 to 1 for the 1 cm cube (6 square cm over 1 cubic cm) and 1.5 to 1 for the 4 cm cube (96 square cm over 64 cubic cm)
  • Explains that the smaller cube has more surface per unit of volume, so materials cross into it faster relative to the volume that needs them

Model answer

The 1 cm cube has a surface area of 6 x 1 x 1 = 6 square cm and a volume of 1 cubic cm, so its ratio is 6 to 1. The 4 cm cube has 6 x 4 x 4 = 96 square cm of surface and 4 x 4 x 4 = 64 cubic cm of volume, so its ratio is 96 to 64, or 1.5 to 1. The small cube has four times as much surface for each unit of volume, so materials crossing its surface reach the volume that needs them faster. A large cell has too little membrane for its volume to keep up.

Apply Apply it

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