Lesson video

Hello, My name's Miss Parnham.

In this lesson, we're going to learn how to find the radius or diameter, given the area of a sector.

Let's find the radius and diameter of this sector.

This sector is three quarters the area of a circle.

So we're going to use that property.

So we know that the area of this sector is 255 millimetres squared.

So if we divide it by three, that will get us the area of a quarter circle with the same radius.

So that gives us 85 millimetres squared.

And then multiplying that by four gets us the area of a complete circle with the same radius.

In effect, we have multiplied by four thirds, but we've broken it down into those two steps.

So now that we know the area of a full circle with the same radius, we can divide by pi.

And this gives us 108, to three significant figures.

Remember, keep that full number on your calculator.

And this gives us the radius squared.

So we need to square root that number.

So now we know that the radius is 10.

4 millimetres to three significant figures.

But look the question wants the diameter as well.

So our final step is to multiply 10.

4 by two and get the answer of 20.

8 millimetres, to three significant figures.

Here's a question 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 was designed really to help you break down the process of finding a radius or a diameter into those single steps.

And then hopefully this will help you with any subsequent questions in this lesson.

Here are some further questions for you to try.

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

Here are the answers.

These questions were all based on sectors that were familiar fractions of a circle.

So finding the area of a circle with the same radius first should have been relatively straightforward.

Now let's look at an example where the angle is not a familiar fraction of 360.

The first thing we're going to do with this sector is divide the area by 212 in order to work out the area of a very small sector with the same radius, but with an angle of one degree.

This gives us an answer of 0.

830 metres squared, to three significant figures.

Please leave the full answer in your calculator because we're going to multiply that by 360 in order to work out the area of a complete circle with the same radius.

This gives us 299 metres squared, again to three significant figures.

Leave that answer your calculator, because what we're going to do now is divide that by pi.

This gives us 95.

1, to three significant figures.

Again, accurate answer in the calculator, please.

Because this is equal to radius squared, in order to find the radius, we need to square root this number.

This gives us 9.

75 metres, to three significant figures.

That is part of our answer, but we also need the diameter.

So let's multiply that own rounded answer by two.

And this gives us a diameter of 19.

5 metres, to three significant figures.

Here's a question for you to try.

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

Here are the answers.

As before, I wanted you to look at a question that was broken down into single steps.

This time we're dealing with a sector, which is not a familiar fraction of a circle, and this question will hopefully help you with ones in later in the lesson.

Here's 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.

Don't forget that that question six need you to find the diameter.

It's really only a simple case of doing exactly as you did with question five, but remembering right at the end to double that radius, to get your diameter.

That's all for this lesson.

Thank you for watching.