Lesson video

Hello, my name's Miss Parnham.

In this lesson, we're going to use the arc length to find the radius or angle of a sector.

Before we find the radius and perimeter of this sector, we need to find the circumference of a circle with exactly the same radius as this sector.

We can find that because we know the fraction of a circle that this sector is, because we know the angle.

So we can form a fraction using 222 degrees over 360 degrees.

19.

4 is the same fraction of the circumference of the complete circle.

So we reverse that process of multiplying the circumference by a fraction to get 19.

4.

So we use the reciprocal fraction of 360 over 222, and that gives us the circumference of a circle with the same radius as this sector, as 31.

5 centimetres.

Now we know that we can divide this by two pi.

This will give us the radius to three significant figures, 5.

01.

Now we know this, the perimeter of this sector is made up of the arc length added to two radii.

So to three significant figures, that's 29.

4 centimetres.

Here are some questions for you to try.

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

Here are the answers.

Did you notice in question one you didn't really need a calculator? Because if you consider circles with the same radius as each sector, then they would have given you circumferences of 24 pi, 36 pi, and eight pi respectively.

So dividing these by two pi to get a radius would give you integer answers every time.

Here are some more questions for you to try.

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

Here are the answers.

Every time we find the radius, it's important to remember to double it before adding on the arc length to get the perimeter.

And make sure the units of measurement for both the radius and the perimeter are the same as those for the arc length that you started with.

In order to find the angle of this sector, we need to first find the circumference of a circle with the same radius of 11 metres.

We do that by multiplying the radius by two and by pi.

This gives us 69.

1 metres.

And because we know the arc length of this sector, then we can form a fraction using the arc length over the circumference.

This is the same fraction that this angle is of 360 degrees.

So if we multiply 360 degrees by the fraction formed from the arc length over the circumference, this will give us the angle of the sector of 100 degrees to three significant figures.

Here are some questions for you to try.

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

Here are the answers.

This question is broken down into single steps to help you think about what fraction the art length is of the circumference of a circle with the same radius as the sector.

The angle in the sector is exactly the same fraction of 360 degrees.

Here are some further questions for you to try.

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

Here are the answers.

These examples show that it is exactly the same process whether we have arc length and radius in millimetres, centimetres, metres, and whether we have an acute, obtuse or reflex angle to find.

That's all for this lesson.

Thank you for watching.