# Lesson video

In progress...

Hello, my name is Miss Parnham and in this lesson, we're going to learn how to find the volume of a cylinder.

Here we have a cylinder and a cylinder belongs to the family of prisms. So the volume of a cylinder is the area of the cross section multiplied by the height.

And in the case of a cylinder, the cross section is always a circle.

So we have pi r squared multiplied by h.

Now in this example, we have a diameter of 15.

So we would have to divide that by two to find our radius.

Our height is eight.

It may puzzle you to call this height because this is oriented in such a way that you might want to call it length.

And you can call it length but we tend to use the word height.

By height we mean the dimension that is perpendicular to the cross section, so on this cylinder perpendicular to the circular face.

So let's put the numbers into the formula.

We have pi multiplied by 7.

5 squared multiplied by eight, which is 56.

25 pi multiplied by eight.

And then we have 450 pi metres cubed and one decimal place that is 1413.

7 metres cubed.

Here are some questions for you to try.

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

A cylinder belongs to the family of prisms so we need to multiply the area of the circular cross section by the height in order to get the volume.

So in the first question that you attempted, this was just a case of finding the product of 12 and eight.

But then in question two, you needed to use pi r squared for the area of the circle and then multiply by h.

Always work with the full accurate numbers in your calculator.

In this example, we're going to find the volume of this cylinder in terms of pi.

So we will not require a calculator and it would be quite possible to get a similar question to this on a non calculator exam paper.

We're going to start in the same way, the volume of a cylinder is the area of the cross section multiplied by the height.

So in the case of a cylinder, that is pi r squared multiplied by h.

Here we have a radius of eight under height of 15.

So if we put those numbers in place of the letters, and we all know that eight squared is 64.

So we have 64 pi multiplied by 15, and that's relatively easy to multiply by 15.

So we have 10 64's and five 64's and that gives us 960 pi and that is centimetres cubed.

Here are some questions for you to try.

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

In question three part a, you needed to find the radius from the diameter.

So in this case it was four and the same with part b, you needed to make sure that you were working with a radius of not.

15.

And then in question four, you needed to watch out for that in part b as well.

So we have a diameter of six and therefore a radius of three and then your cross section will be nine pi and then multiply by 10.

That's where the answer of 90 pi comes from.

Here's a quick question for you to try.

Pause the video, to have a go and then restart the video when you're finished.

Did you notice in the formula, there is the diameter instead of the radius.

So instead of pi multiplied by 10 squared multiplied by seven divided by two, we needed to have written time multiply by five squared, multiply by seven, all divided by two.

And that gives us a accurate answer of 87.

5 pi millimetres cubed.

That's all for this lesson.

Thank you for what watching.