Lesson video

Hi, everyone.

I'm Mr. Lund, and in this video, we're going to be calculating the circumference of circles.

Hi, everyone, let's recap parts of the circle.

Here is the circumference of the circle.

Here is the diameter.

The diameter is a straight line that travels from a point on the circumference of a circle through the centre of the circle to another point on the circumference.

Here's the radius.

The radius is a straight line that travels from the centre of the circle to a point on the circumference.

What is the connection between the diameter and the radius of a circle? Do you know, the diameter is double the radius? The radius is therefore half the diameter.

What is the formula for this circumference of a circle? There's a connection between the circumference of a circle and its diameter.

The diameter fits in around about three times.

This around about number is called pi.

The circumference is pi times the diameter.

If I have a circle, where the diameter was 20 centimetres, I can estimate the circumference of this circle by saying, well if the circumference is pi times the diameter, let's say the circumference is around about three times by 20.

So the circumference is around about 60 centimetres.

Estimating is a useful tool to check that we've got the correct answers when we start using pi.

Pi is a peculiar number.

So much so that they call it irrational.

It goes on forever and ever, and this makes calculations tricky.

So, to make life easy, we can display calculations in terms of pi.

Let's find the circumference in terms of pi.

Here's the formula.

Circumference equals pi times by diameter.

The diameter in our circle is 20 centimetres.

So the circumference is pi multiplied by 20.

Here we go.

That's how we would display our answer.

Don't forget your units.

You also need to be able to display your answers numerically.

Let's find the circumference of this circle to one decimal place.

The circumference is pi times by the diameter.

You need to memorise this formula.

If the circumference equals pi times by 20, then the circumference is equal to 62.

83185, and so on.

Remember, pi is a number that never ends.

So, we can only ever really get an estimate.

The circumference to one decimal place would be 62.

8 centimetres.

Don't forget your units.

Have a look at this example.

What's the same and what's different about this circle? Do you see, the radius is 20 centimetres in this example? What does that tell us about the diameter of the circle? The diameter is twice the length of the radius.

So the diameter is 40 centimetres.

Let's find the circumference of this circle to three significant figures.

Here is a formula.

Circumference equals pi times by diameter.

It's useful to always write that down in your exam to help you.

The circumference is pi times by 40.

That gives us this answer.

But to three significant figures, we can round our answer to say 126 centimetres.

Here's some examples for you to try.

Write down the formula first, and then try and work out the circumference of the circles in terms of pi.

Pause the video and return to check your answers.

Here are the solutions to questions one, two.

Did you know that the letter pi is the Greek letter for P? Think of showing things in terms of pi as though you are using algebra.

Let's try question three.

Pause the video and return to check your answers.

Here are the solutions to questions three.

Rounding to three significant figures is a skill that you need to practise and to achieve precisely.

Pause the video and return to check your answers.

Here's the solutions to questions four and five.

How did you do? In question five, did you notice that the units were different? It was easy to order them from that understanding.

Well done for getting this far.

Here's a bonus question.

How do you find the perimeter of a semi-circle? The arc of a semi-circle is half of the conference of the entire circle.

This length is the diameter of the circle.

So if I can find half of the circumference of the circle, and add it to the diameter of the circle, then I can find the perimeter of this semi-circle.

Here's the calculations I would make.

First of all, write down your formula.

Circumference equals pi times the diameter.

I can calculate the circumference to be 21.

99 etcetera.

By dividing that in two finds me the arc of the semi-circle.

Let's round our answer to two significant figures.

The perimeter is therefore the arc plus the diameter, which equals around about 18 metres.

Here is two more questions for you to try.

Well done for getting this far.

Pause the video and return to check your answers.

Well done for getting to questions six and seven.

These are a little bit more complicated.

Question seven, there's a lot of working out to do.

So make sure you write down all the steps.