Surface Area of Cylinders

Today we looked at the total surface area of a cylinder. A cylinder looks like this:

The two pieces of information we need to find the total surface area of a cylinder are the radius (marked with an "r" on the diagram above) and the height of the cylinder (marked with a "h" on the diagram above). Remember, the radius is only half way across the circle, so if you are told the full distance across the circle you will need to half this. 

To find the surface area, imagine this cylinder all folded out as a flat 2D shape. We call this a net. The net of a cylinder looks like this: 

From this we can see that a cylinder is simply 2 circles and a rectangle. We know how to find the area of both of these. We know the area of a circle is: 

We have two of these circles, so the total area of the two circles is two lots of this, or:

Now we need to find the area of the rectangle part. For the area of a rectangle, we need the length and the width. We already know the length. This is the height of the cylinder (marked "h" on our cylinder and the net of the cylinder). We now need to find the width of this rectangle. If you look carefully you will see that the width is actually the same as the distance around the outside of the circle. This is known as the circumference of a circle. The formula for finding this is simply: 

So this is our width, and we know that the height of our rectangle is its length, so the total area of the rectangle can be found by multiplying these two together. We get:

So finally, to get the total surface area of the cylinder we combine the area of this rectangle by the area of the two circular pieces. This gives us a final formula of;

We can use this now to easily find the surface area of a cylinder. All we need to do is substitute the length of the radius (r) and the height of our cylinder (h) into this formula and use your calculator to get an answer for the total surface area. 

You should now be able to finish off most of the work from the surface area section of the worksheet. You can find a copy of this worksheet in the "Worksheets" tab. It is the first worksheet on surface area and volume. 

If you have any questions about this feel free to comment on this post, or email or chat to me in person.