Week 4 · Assignment: Traditional alternative (no AI)

Week 4 — How Big Can a Cell Get? The Cell-Size Report — Traditional alternative (no AI)

Introduction to Biology Free sample edition

Traditional alternative (no AI), unpublished. In the course this is a separate assignment that ships unpublished beside the adaptive assignment: same objective, no AI. An instructor who prefers it publishes it and unpublishes or deletes the adaptive one, as the note at its top says.

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 4 of the term — compute how a cell's surface, volume, and pump work scale, and explain to someone new to biology why cells stay small.

This week you sorted cells into two kinds, toured the organelles, followed what crosses the plasma membrane, and used the cube cell to see why cells stay small. In this assignment you work four short problems, interpret each one, and explain the size limit to someone who has never studied biology. This week's lecture tutorial, quiz, discussion, and Biology Lab & Inquiry practise the same ideas from other angles. It builds on Week 3, where you met the phospholipid that the membrane is made from.

The task

The cube cell is an illustrative model built for this course (not real data). Four model cube cells have sides of 1, 2, 3, and 4 units. For a cube of side s, surface area = 6s², volume = s³, and the surface-area-to-volume ratio simplifies to 6 ÷ s, so the four ratios are 6:1, 3:1, 2:1, and 1.5:1. The sodium-potassium pump spends 1 ATP in each cycle to move 3 sodium ions (Na⁺) out of the cell and 2 potassium ions (K⁺) in.

Work these four problems, showing your arithmetic:

A model cube cell has a side of 2 units. Using surface area = 6 × side × side, what is its surface area in square units?
The side-4 model cube cell has a surface area of 96 square units and a volume of 64 cubic units. What is its surface-area-to-volume ratio?
The sodium-potassium pump moves 3 sodium ions out of the cell in each cycle and spends 1 ATP per cycle. How many sodium ions does it move out in 4 cycles?
When the model cube cell's side doubles from 2 to 4 units, its surface area goes from 24 to 96 square units. How many times larger is the new surface area?

Beside each answer, add one brief interpretation:

Problem 1: say what surface area stands for in a real cell, and explain what it means that the plasma membrane is selectively permeable.
Problem 2: write the ratio in simplest form, compare it with the side-1 cube's 6:1, and explain why a falling ratio limits how big a cell can get.
Problem 3: explain why the pump counts as active transport, and contrast it with facilitated diffusion.
Problem 4: compare this growth in surface area with the growth in volume (8 to 64 cubic units), and name one way real cells cope, giving an organelle that uses it.

Explain it to a non-expert

Your younger sibling, after a science video, asks, "Why can't one cell grow as big as a basketball?" Write a 3–5 sentence message that explains the size limit in everyday words using your results, and names one limit of the evidence, including that the cube cell is an illustrative model and that real cells are not cubes. Explain any technical term in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a friend asking why crushed ice cools a drink faster than one big ice cube. Model answer: "Ice cools a drink only where it touches the drink, at its surface. Crushing one big cube into many small pieces keeps the same amount of ice but gives it far more surface touching the drink, so heat moves faster. That is why the crushed ice works quicker even though there is no more of it. Ice is not alive, so this comparison shows the surface idea but not how a living cell takes in food or water."

Use that pattern for the cell-size question, with your own wording and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the values in the problems without guessing which values or steps you used.

Deliverables

Submit a single report containing:

the four answers, each with the arithmetic shown and the brief interpretation the task names for that problem;
your message to your sibling, explaining the size limit in everyday words and one limit of the evidence; and
a one-line restatement of the cube-cell formulas you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled sketch of the cube cells with a short note. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the arithmetic, the interpretations, and the writing yourself, without a chatbot or other AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's work, is an integrity violation under the course policy.

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