When you picture a cell, it is likely that you picture a eukaryotic (this means true kernel - kernel refers to the nucleus at the center) cell - one with a nucleus. However, this excludes a huge group of cells known as the prokaryotic cells. Prokaryotic (this means before kernel because these cell evolved first, before the nucleus evolved) cells lack a nucleus, and most other organelles.
You probably know that cells are incredibly small. However, it is important to think about how large they might be compared to one another. Why is that? Well, we need to take a quick look at some basic mathematics.
Let's think about a balloon as an analogy. If I have a balloon that has air in it, it can act kind of like a cell. The latex that surrounds the air, trapping it in, is much like a cell membrane.
Okay, so I have one balloon like the one shown above. Let's imagine that I get another balloon, but this time I blow it up even more than the first balloon was filled, as shown here. Let's compare these balloons.
The balloon on the left is bigger, right? Well, that's obvious. But when we look at shapes like these, there are two quantities I want you to think about. First is a cell's (or in this case, a balloon's) surface area, or the area of the surface between the inside and the outside. On the balloon, imagine if I could measure exactly how much latex the air was able to touch. That would be my surface area of the balloon. As the balloon increases in size, the surface area increases. So, the balloon on the left has a higher surface area than the balloon on the right. Surface area is an area, so it is measured in m2 or cm2.
The second quantity that we need to keep in mind with these cells and balloons is the volume, or the space that the object takes up. The volume of the balloon is easily visualized - it represents how much air is inside of the balloon. So, as a balloon increases in size, its volume increases. Cells do the same thing. Volume is measured in m3 or cm3.
So if both of these quantities increase as cells or balloons enlarge, why does it matter? Well, let's think about the units. surface area is measured in meters squared, whereas volume is measured in meters cubed. So, let's ignore the balloon for now and think about a simpler shape - a cube. In the image shown, the cube on the right is just like any cube with equal length of all sides.
In this particular case, that length is 1 cm (the units are not listed in the image because it is best to focus on just the number for now). If the side length is 1 cm, then the surface area of that cube on the right is 6 centimeters squared, because there are six sides to a cube. You have to find the area of one side (1 cm x 1 cm = 1 cm2), and multiply it by those 6 sides. So the total surface area of the right cube is 6 cm2. The volume is calculated by multiplying length x width x height. This is, of course, 1 cm x 1 cm x 1 cm = 1 cm3.
Now, let's look at the cube on the left. The length of this cube is 3 cm. So the sides are 3 times as long as those of the first cube. As a result, we can calculate the surface area and volume just like before. Doing so yields a volume of 27 cm3 and a surface area of 54 cm2 .
If you look closely, you can see that the shape's volume is increasing at a faster rate than its surface area. That's because surface area is calculated by squaring a side length (and multiplying by 6), whereas volume is calculated by cubing a side length. So doubling a side length actually increases surface area by a factor of 4 (because double is 2, and 2 squared is 4), whereas it increases the volume by a factor of 8 (because 2 cubed is 8). So volume increases much faster than surface area.
This is referred to as the surface law, and it explains a shocking amount about you. Think about a balloon: when a balloon is empty, it is mostly rubber with little to no air inside. When it is blown up, it becomes mostly air with a relatively small amount of rubber on the outside. "The more you inflate it, the more its interior dominates the whole." One implication of the importance of the surface law is with body temperature. Heat is lost at the surface, so the more surface area you have relative to volume, the harder it is to stay warm. Source: The Body: A Guide for Occupants by the excellent Bill Bryson.
Okay, now we can see that volume increases faster than surface area does. Why do I care? Well, a very important number when it comes to cells (and everything from food to roots) is their surface-area-to-volume ratio. Have you ever noticed how you taste food a lot more after you've chewed on it a bit? You are breaking a large cube (let's simplify to cubes again) into a lot of smaller cubes. That means a lot more surface area is able to interact with your tongue. This means you taste more when there is more surface area.
This ratio matters for cells because the surface area is the way by which a cell interacts with its environment - this is how it obtains its resources. If a cell needs to take in some molecule, that molecule can only get in by interacting with the surface area (the cell membrane). If a cell is large, it needs more resources. So, it needs a higher surface area. If it gets so big that the volume is horrendously large, the resources needed by the cell are equally horrendous. As it grew, the cell was able to take in more resources due to its higher surface area. But the demand increases faster than the supply, because volume increases faster than surface area.
If you need to calculate the surface-area-to-volume ratio in order to compare two cells, you simply need to divide surface area by volume.
One of the ways by which cells are able to get larger despite their increased energy demands is by utilizing specialized organelles. Organelles are basically specialized components of a cell - basically they are parts of a cell that have a single or a small number of jobs to perform.
Just like in all of biology, function is dependent on structure, so as you look at specific organelles, it is important to think about why they may be shaped how they are, contain the membranes they have, etc.
You are responsible for being familiar with all of the organelles shown in this diagram. Rather than reiterating all of the information about them here, however, please reference the lecture I have made for simplified explanations and diagrams. There is also a simplified chart provided here for a less-detailed account of some of the important organelles to be familiar with.
As a quick reminder when using the table provided:
Eukaryotic cells are cells that have a nucleus
Prokaryotic cells do not contain a nucleus