CEL - Cell Size [LESSON]

Cell Size

Introductory Lab Activity 

Use the video lab to investigate three different “cell” sizes.

There are three different size agar cubes that represent cells of different sizes. Agar is simply a Jell-O-like substance that dissolves in water when heated up and solidifies when it cools back down.

These particular agar cubes also had some phenolphthalein mixed in while they were still liquid. Phenolphthalein is an indicator chemical that detects the presence of acids and bases (this chemical is a clear color in acidic/neutral pH and pink in basic pH).

The different agar cubes have already been pre-soaked in a dilute base (0.1 M NaOH). Thus, the cubes are fully pink inside (the base has already diffused into all parts of the cube). The video shows the process of soaking these pink cubes in an acidic solution (0.1 M HCl).  As the acid diffuses in, it will neutralize the base and turn that part of the cube clear again. 

We will use this chemistry to model the entry of nutrients into cells that need them. Watch the video below to view the diffusion process – pay close attention to the differences between the three cubes.  

Which cell got the nutrients that it needed?

You can see that the smaller cell became clear much faster than the others. That’s because the smaller the cell, the LARGER the surface area to volume ratio.

You can see that the smaller cell became clear much faster than the others.  That’s because the smaller the cell, the LARGER the surface area to volume ratio. Let’s calculate the surface area to volume ratio for each of the three cells.

Image shows a small cube with side length 1, a medium cube with side length 2, and a large cube with side length 3.

You can see the small cube has a surface area to volume ratio of 6:1, the medium cube 3:1, and the large cube 2:1.  What happens to this ratio as cell size increases? The ratio INCREASES. So the smaller the cell, the higher the surface area to volume ratio.

Why are cells small?

Cells need to maximize their surface area and minimize their volume in order to ensure that there is adequate surface for the transport of materials into the cell (that the cell needs) and the transport of waste out of the cell. As cells grow, they increase in volume faster than they increase in surface area. This limits the balance of nutrient intake and waste output. Materials must be able to reach all parts of a cell and waste must be able to diffuse out quickly but when the volume of a cell is too large relative to the surface area, diffusion cannot occur at sufficiently high rates to accommodate the entire cell. 

Math Skill: Calculate the surface area to volume ratio of different cell shapes

 First, watch this Surface Area to Volume video to understand what is happening mathematically as cell size increases.

Here is an image of the surface area and volume calculations expected by the College Board.

This image shows the surface area and volume equations for a cube, sphere, cylinder, and rectangular solid.

Now, practice using the surface area to volume ratio equations below. You should be able to calculate the surface area, volume, and surface area to volume ratio for any of these shapes.

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