Why cells are small

A question about size

An elephant has the same kinds of cells as a mouse. But an elephant is not made of larger cells. It is made of more cells. Why do cells stay small?

Surface and volume

A cell takes in food and oxygen through its surface, and it uses them inside, in all of its volume. So a cell works well only if its surface is big enough for its volume.

Let us test this with a cube. A cube with side $L$ has

The ratio of the surface area to the volume is

When $L$ gets bigger, the ratio $\dfrac{6}{L}$ gets smaller.

The cube of side 1 cm has 6 cm² of surface for each 1 cm³ of volume. The cube of side 4 cm has only 1.5 cm² for each 1 cm³.

You should find that the ratio halves every time the side doubles. A cell of side 0.5 µm has 12 µm² of surface for each 1 µm³; a cell of side 10 µm has only 0.6.

What this means for a cell

If a cell becomes twice as wide, its volume becomes 8 times as large, but its surface area only 4 times. The surface cannot bring in enough food and oxygen for all that volume, and waste leaves too slowly.

So a cell cannot grow very large. When it reaches a certain size, it divides into two new cells. This is how a body grows: by making more cells, not bigger cells.

Try it in Python

This program makes a table for cubes with sides from 1 cm to 6 cm.

Shapes that help

Some cells are not round. Their shape gives a large surface for their volume.

• A root hair cell has a long thin part that goes into the soil, and takes in water through a large surface.
• A red blood cell is flat with a dent in the middle, so oxygen has a short way to go to the centre.
• A nerve cell can be more than 1 m long, but it is very thin, so its volume is small for its length.

Some cells are large, such as an egg cell, because they store food. They do not work hard, so they do not need a fast supply.

Practise with new numbers

Common mistakes

• Thinking surface and volume grow at the same rate. Doubling the side makes the area 4 times and the volume 8 times.
• Forgetting the units of the ratio. It is "per µm", or "per cm".
• Thinking every cell is round. Many cells have shapes that give more surface.
• Thinking a large egg cell breaks the rule. It stores food and does little work.

Remember these

• For a cube, the ratio of surface area to volume is 6 ÷ side. It falls when the side grows.
• A cell takes in materials through its surface and uses them in its volume, so a large cell has a problem.
• Cells divide when they are large, and many cells have shapes with a large surface.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A cube cell has a side of 3 µm. Find its surface area, volume and ratio.

2. A cell grows to twice the width. By how many times does its volume grow?

3. Why does a root hair cell have a long thin part?

4. Why is an elephant not made of giant cells?