Agar Cube Diffusion Virtual Lab: Surface Area to Volume

This agar cube diffusion virtual lab runs the classic surface area to volume practical from GCSE, IGCSE, A-level, IB and AP Biology. Pink agar, made with dilute sodium hydroxide and phenolphthalein, is cut into cubes of 0.5, 1, 2 and 3 cm and dropped into hydrochloric acid. The acid diffuses in from every face and the pink clears from the outside in. Students record how long each cube takes to turn colorless and how much of it the acid reaches in 10 minutes, then calculate SA:V. A second set of blocks with the same volume but different shapes links the results to villi, alveoli and leaves.

Curriculum links

• AP Biology Unit 2, topic 2.3 Cell Size (ENE-1.B, ENE-1.C): the effect of surface area-to-volume ratio on the exchange of materials.
• AQA GCSE Biology 4.1.3.1 (diffusion): calculate and compare surface area to volume ratios. AQA A-level Biology 7402, 3.3.1: surface area to volume ratio.
• IB Biology (first assessment 2025), B2.3: surface area-to-volume ratio as a constraint on cell size.

Simulic is not affiliated with or endorsed by the College Board, AQA or the International Baccalaureate.

Before the lab (5 min)

Ask students to commit to a prediction, on paper or as question 1 of the class link:

"In 0.1 mol/dm³ acid, a 1 cm cube turns colorless in about 11 minutes. How long will a 2 cm cube take?"

Offer about 11, 22, 44 or 88 minutes. Most students choose 22.

Method in the simulation

1. Keep Agar blocks on Cubes 0.5, 1, 2, 3 cm, Hydrochloric acid on 0.1 mol/dm³ and Fixed time at 10 min. Set Speed to 1 s = 5 min.
2. Calculate SA = 6a², V = a³ and SA:V for each cube, then check them against the table.
3. Press Add acid and start. Tick Cut blocks in half to see the pink cores shrink.
4. When the run ends (or after Skip to end), record the % of volume reached after 10 min and the time to turn colorless.
5. Switch Graph to SA:V and time against side.
6. Change Agar blocks to Same volume (8 cm³), different shapes and repeat steps 3–4.

Side (cm)	SA (cm²)	V (cm³)	SA:V (cm⁻¹)	% reached after 10 min	Time to turn colorless (min)
0.5
1
2
3

Expected results

All values were read from the simulation (0.1 mol/dm³ acid).

Side (cm)	SA (cm²)	V (cm³)	SA:V (cm⁻¹)	% reached after 10 min	Time (min)
0.5	1.50	0.125	12.00	100	2.8
1	6.00	1.00	6.00	100	11.1
2	24.0	8.00	3.00	85	44.4
3	54.0	27.0	2.00	68	100.0

• Each doubling of the side halves SA:V and makes the time four times longer: 11.1 → 44.4 min. The acid front moves as depth = k√t, so twice the distance to the center takes four times as long.
• Same volume, different shapes (8 cm³ each): the 2 × 2 × 2 cube (SA:V 3.00) takes 44.4 min, the 4 × 2 × 1 block (3.50) takes 11.1 min, the 4 × 4 × 0.5 sheet (5.00) takes 2.8 min, and eight 1 cm cubes (6.00) take 11.1 min.
• At 1 mol/dm³ every time is ten times shorter: 0.3, 1.1, 4.4 and 10.0 min.

Questions for students

1. (Prediction, asked again after the lab) How long does the 2 cm cube take to turn colorless?
2. Which is a control variable?
3. What % of the 3 cm cube's volume does the acid reach after 10 min?
4. How many times faster does the 4 × 4 × 0.5 cm sheet clear than the 2 cm cube?
5. Explain how the results show why large organisms need exchange surfaces.

Answers for teachers: (1) About 44 min, four times the 1 cm cube. (2) The acid concentration (also its temperature and volume). (3) 68% (accept 67–69). (4) 44.4 ÷ 2.8 = 16 (accept 15–17). (5) As size rises, volume grows faster than surface area, so SA:V falls and the center lies further from the surface; diffusion alone takes too long. Flattening or folding the surface (villi, alveoli, leaves) raises SA:V and shortens the distance, and transport systems carry substances the rest of the way.

Common misconceptions

• "The big cube has more surface, so it clears faster." The 3 cm cube has nine times the area of the 1 cm cube but 27 times the volume. It takes 100 minutes, not 11.
• "Twice the size, twice the time." Doubling the side makes it four times longer.
• "Same volume, same time." The four 8 cm³ blocks clear in anything from 2.8 to 44.4 min.

Extension

• Set Hydrochloric acid to 1 mol/dm³: why do the times change but not the pattern?
• Use the surface area to volume mode of Levels of organization to find SA:V for real cells.

FAQ

Why does the 4 × 2 × 1 block clear as fast as the 1 cm cube?

The time depends only on the smallest dimension. Both blocks are 1 cm thick, so the acid reaches their middle after the same 0.5 cm, in 11.1 min.

Can students cut their own blocks?

Yes. Choose Cut your own blocks, set the Shape, Side or the cuboid sizes, and press Cut and add (up to five blocks). In the link's starting values you can pin Agar blocks and Cube side (Cut your own blocks).

Are the times realistic?

The model is tuned so a 1 cm cube clears in about 11 min, a typical class result. Real times vary with the agar recipe and temperature.

Related simulations and guides

Levels of organization – from cell to organism Diffusion across membranes and osmosis in cells

For another diffusion practical, see the osmosis virtual lab. For more topics, see interactive biology lesson ideas.