Lesson video

Hello, I'm Mr Coward, and welcome to today's lesson on area of sectors.

So today's lesson, you will need a pen and paper or something to write on and with and a calculator.

If you could please take a moment to clear away any distractions, including turning off any notifications that would be great.

And if you can try to find a quiet space to work, where you won't be disturbed.

Okay, when you're ready, let's begin.

Okay, so time for the Try this task.

These circles are all different sizes and not drawn to scale.

So as you can tell by the radius, they all have a different size radius.

Now you can they are not to scale cause 16 is definitely not the same as two.

That circle would be much bigger than this circle.

However, I've made them all the same size, just so it's easier so that everyone could see it.

So, what circle would have the biggest area shaded? Have a go, see if you can workout what area shaded.

See if you can predict before you work out.

Does your answer surprise you? So pause the video and have a go in three, two, one.

Okay, welcome back.

Here are my answers.

So two times two pi, four pi.

Four times four pi, 16 pi and then half of the circle so eight pi.

This one, the full circle would be 64 pi so a quarter of the circle is 16 pi.

The full circle would be, I'm not sure what 16 squared is, I think it's 256.

Let me check.

16 squared, 256.

Yeah.

So then 1/8 of the circle would be 32.

So did that surprise you? Maybe it did.

Maybe it didn't But if it surprised you, did you think that they would all be the same? Cause I know that quite a few people would but from last time, we kind of saw that , it doesn't quite work like we would expect when we're dealing with the area.

So that's just a little something to have a think about.

And in fact there's also somewhere else we could think right.

If we have 1/2 a circle of this one and half a circle for this one and half a circle for this one, what would our numbers be? Would there be pattern there? And what is this pattern? Why are they always getting two times bigger? But we're getting half the amount of pieces on each time.

Lets get it two times bigger.

Well, our area of these circles is actually getting four times bigger and that's to do with scale factors which I alluded to last time.

And I'm still not going to tell you exactly why it works this time unfortunately but that would just mean you are super excited and you're super keen to when you do scale factors in the future.

Okay.

So we're going to to find the area of these sectors to two decimal places.

Wow.

So like before, when we were doing out length, we need to find out what fraction of the full circle lies and then multiply that fraction by the area of the full circle to get that sector.

So what fraction of the circle is it? Well, 72 out of 360 degrees.

So that is what fraction of the circle is.

Okay.

Now what would be the area of the full circle? Well it would be, so area of the full circle would be five pi times five, 25 pi.

So we would get, we work that out and we would get five pi or to two decimal places, 15.

71.

Our units would be, oh, we don't have units actually, do we? so let's just leave it like that.

Okay.

You have to find the area of this sector.

So pause the video and have a go, pause in three, two, one.

Okay.

Welcome back.

Now hopefully you've worked this out correctly and you got an area of, if am told to write the calculation down, 113 divided by 360 times 25 pi cause our two circles are the same.

So they'd have the same area which should have got you 24.

65 to two decimal places.

So really am not doubting if you got that correct.

Just be careful with your rounding as well.

Okay.

Find the area of these sectors to two decimal places.

So I've got one on you and one's hidden for now.

So what fraction of a full circle would it be? 102 out of the full circle 360, times by, what would the area of the full circle be? Well, we've got six and am going to write this around for now.

six times six pi, so that would be 36 pi.

So my area would be 102 divided by 360, times by 36 pi which would give me an answer of 32.

04 to two decimal places.

Okay.

So your turn.

we'll cut the area of this sector.

Okay.

Welcome back.

Hopefully you correctly worked out the area and it was 220 divided by 360 times by 64 pi, which gives you 122.

87 to two decimal places.

Okay.

So really well done if you got that correct.

And again, we have no units, so I've put no units on the answers.

Find the area of these sectors in exact form.

So what fraction of the circle is that? It's a quarter circle cause it's 90 degrees.

90 out of 360 is a quarter.

So a quarter of a circle, what would the area of the full circle be, 12 times 12 pi, 144 pi.

So a 1/4 of 144 pi.

So half of that is 72, half of 72 is 36.

So it's 36 pi.

Okay.

So your turn.

Find the area of these sectors in exact form.

So it must be in terms of pi, if it's exact.

So pause the video and have a go in three, two, one.

Okay.

Welcome back.

So hopefully you worked out the full circle.

It would be 64 pi and then you have 3/4 of 64.

So one quarter is 16.

So three quarters is 48 pi.

So really well done if you got that correct.

Okay.

So now it's time for the independent task.

So pause the video to complete your task and resume once you've finished.

Okay.

Well, come back here are my answers.

You may need to pause the video to Mark your work.

Okay, and now it is just time for the explore task.

So, pause the video to complete your task and resume once you've finished.

Okay.

Welcome back.

So the first thing we need to do is we need to find the area of the full circle.

So this circle has a radius of six.

So the area of the full circle is six times six pi, which gives us 36 pi, okay? pi times pir or pir times r, multiplications permits this so that we can write in whichever way round.

Find area of the green sector.

Okay.

While the full circle is 36, we take that away, we've got 30 left.

We take that away, we've got three pi left.

So that must be three pi because 36 minus 33, so 36 pi minus 33, which is what we've already got, gives us the green sector as three pi.

What fraction of the circle is blue, pink and green? For blue, we have 27 pi out of the total 36 pi.

So that's the same as 27 out of 36, which simplifies to 3/4.

So if that's 3/4 of the circle, that angle there must be 270 degrees.

Okay next for the pink.

What's six pi out of 36 pi.

What does that simplify to? Well, the pis simplify.

So we get six out of 36, which is 1/6.

So 1/6 of 360 is 60 degrees.

And the green section, well, that is a 1/3, sorry.

That is three out of 36, which simplifies to, that's going to be a pi there, three out of 36 pi, which simplifies to 1/12.

So what angle is that? That would be 30 unless checked.

Yeah, they add up to 360.

So that's good.

So it's always good to do a little check on things like that.

Now what would the size of the sectors be if the angles were, and I left that as an open question for you to try different angles and work things out.

So hopefully you had to play around with that and came up with a few questions of your own.

So, that is all for this lesson really well done.

Thank you very much for all your hard work and I'll see you next time.

Thank you.