Lesson video

My name is Miss Parnham.

And in this lesson we will be calculating the surface area of cylinders.

Lets work out the surface area of a cylinder.

This is the total area of all its faces.

We can do that by using a net.

So first consider the curved surface of a cylinder.

It is in actual fact a rectangle curved around to meet at the circumference of the circular faces, top and bottom.

So the length of that rectangle is the circumference.

On the other dimension of it is the height.

We know the formula for the circumference is either pi d or two pi r.

So multiplying the circumference and the height together gives us an expression of two pirh.

Now let's consider those circular faces.

The first one at the top is of course pi r squared.

And then there's an identical circle at the bottom, which is of course pi r squared again.

So the surface area of a cylinder is these three distinct areas added together.

We can make this a little bit simpler.

We can see straight away that we've got two pi r squared.

So we can write the surface area like this.

And you could if you wanted, instead of writing two pi rh you could write pi dh.

That would be fine, but I've left it like this because we can actually factorise this.

And some people prefer the surface area formula in this form.

Now let's use this to find the surface area of this cylinder.

So we can see here, we have a height of 13, a diameter of 10, and therefore a radius of five.

So we will put our values of 13 in for h, and five in for r in our surface area formula.

So we can add five and 13 together there to make 18, two pi multiplied by five of course gives us 10 pi.

And this is relatively easy to multiply together.

It's 180 pi centimetres squared.

If you want to do that on a calculator to three significant figures, that is 565 centimetres squared.

Here's a question for you to try.

Pause the video to complete the task, and then restart the video once you're finished.

Here are the answers.

Hopefully this question helps you to see that we can break questions like this down into steps, and work out the area of the individual faces before summing them to get our final solution.

Here are some more questions for you to try.

Pause the video to complete the task, and then restart the video when you're finished.

Here are the answers.

It is very important to work with accurate numbers, and only round the answer at the very end.

And one way to do that is to leave a number in terms of pi for as long as possible.

So, for example, in question two a we have a diameter of eight, which means we have a radius of four, and four squared multiplied by pi gives us 16 pi.

So we have 16 pi at one end of the cylinder, and 16 pi at the other.

And the rectangular face that wraps around has got dimensions 10 and then eight pi for the section that wraps around the circular faces so that has got an area of eight times 10 pi or 80 pi.

So we have two lots of 16 pi, 80 Pi, we've got 112 pi, and then pop that in your calculator, and to three significant figures that is 352 metres squared.

Here's a quick question for you to try.

Pause the video to complete the task, and then restart the video when you're finished.

Did you spot the mistake? So the surface area of the complete cylinder is 120 pi.

If we have that, this will only give us the surface area of the two semicircular cross sections, and the curved surface.

We need to remember the flat rectangular surface.

So onto 60 pi we would have to add seven tens, which is 70 millimetres squared.

That's all for this lesson.

Thank you for watching.