Area of a circle - math lesson - Free Educational videos for Students in K-12

Area of a circle - math lesson - By tecmath

Transcript


00:0-1	get a welcome the Tech Math channel . I'm josh
00:02	in this video . We're going to be looking at
00:03	how to work out the area of a circle .
00:05	So we're gonna start out by just looking at the
00:06	different parts of a circle that you need to know
00:08	and then how to follow the formula to work out
00:11	area of a circle . So let's get on to
00:13	that . So over here we have a circle and
00:16	first I'm going to draw your attention to this particular
00:18	measurement with a circle . It's very important is from
00:21	the center to the very edge . Now , pretty
00:24	much if you put a point in the center and
00:26	then come out of certain distance and then follow the
00:28	distance all the way around , that's how you get
00:30	a circle . This distance here is called the radius
00:35	. So first off , I'm going to just mark
00:37	that in quite often . We call this just for
00:39	the radius . The other distance , which is really
00:42	important to know is this one here , which is
00:44	a distance right across . Quite often , if you
00:47	see a circle we're gonna be talking in terms of
00:49	how big the radius is , but you actually talk
00:52	about how large or how far across that circle is
00:55	. So as you can imagine , that's a pretty
00:58	important one to know . And this here is called
01:01	the diameter . So often this is the way we
01:04	will think about how big a circle is . But
01:06	a bit later on when we're calculating , we're going
01:08	to be using that radius and as you can probably
01:10	see the radius , well , that's half the size
01:13	of the diameter . The other important one to know
01:16	is this particular measurement around the outside here , which
01:21	is you can think of as a perimeter , but
01:22	it's also called this conference . We're not going to
01:26	be using this when we actually go to work out
01:29	the actual area , but it's an important one to
01:31	know when we're dealing with circles anyway . And all
01:34	the way around this is the circumference . So cool
01:39	. How do we go about working out area of
01:42	a circle ? Now ? It's pretty simple . There's
01:44	a formula you're going to be using here and it
01:46	is as follows , it goes on this , the
01:48	area of a circle is equal to pi radius squared
01:53	to pi times radius square . There's a couple of
01:55	things I just want to draw your attention to because
01:57	I see students make these mistakes . First off ,
02:00	we'll go through this particular little are , you know
02:03	, part of the formula here we have pie here
02:05	, Pie , what is pi If you look at
02:07	the diameter and the circumference here and you go ,
02:10	okay , what's the ratio between two ? That is
02:12	to say . You get the circumference divided by the
02:14	diameter . You get this figure here , this constant
02:16	, which is called pie . It's around about 3.14159
02:21	so on and so forth , and it keeps going
02:23	and going and going . It's just a number that
02:26	we use is 3.1415 number that we use to work
02:29	out things like say the distance around the circle ,
02:31	the circumference and the area of a circle . It's
02:34	not only used in circles , it's used in some
02:35	other things , but definitely if you have a circle
02:38	and you're working and say something like a sphere or
02:39	something like a cylinder , this pie will be coming
02:43	up . Okay , this constant will come up .
02:45	So what you do is you get to work out
02:47	the area , you're gonna get pie this 3.14 and
02:49	you're going to multiply it by the radius , That's
02:52	the radius . Remember here , square , this is
02:54	the radius times the radius . And a big thing
02:56	I've seen a lot of students do don't make this
02:59	mistake , it is not the radius times to okay
03:02	, this to here doesn't mean multiplied by two ,
03:04	it means squared , it means the radius times by
03:07	itself . So that's how you go through and you
03:10	work out the area of a circle . So I
03:12	guess what about an example here ? So say for
03:15	instance , we had the following say we have a
03:17	circle here and we want to work out its area
03:20	within the circle and we know that the radius is
03:22	equal to five centimeters from the center to the er
03:25	is five centimeters . How we're going to work it
03:28	out ? Well , it's pretty simple . We're going
03:30	to follow the area equals pi r squared . This
03:32	formula will come through again and again and again .
03:34	If you can remember this formula , everything is pretty
03:36	good . Now quite often You're gonna have this number
03:39	pi on your calculator . So when you hit pie
03:42	, that's going to come in at 3.14 , right
03:45	Right through . If you use around version of it
03:48	and call it 3.14 , you're gonna probably maybe be
03:51	a few decimal places out . So as much as
03:54	possible use the actual figure of pie . But if
03:57	you have to 3.14159 is you know , I'll get
04:01	your fairly close . So this is times the radius
04:04	which is 5cm times the radius once again which is
04:08	five centimeters . So what do we get when we
04:11	get that ? Well you can do that , you
04:12	can go pi 3.14159 blah blah blah blah blah times
04:15	five times five . And we get the area of
04:20	78.54 centimeters squared . And that's the first type of
04:26	question you'll get when you're working at the area of
04:28	a circle . Pretty simple . You get the radius
04:30	, you'll square it and then you multiply it by
04:32	pi and that's pretty simple . Right ? What about
04:36	we look at another type of questions that's fairly common
04:38	when you are looking at circles . Okay , here's
04:40	an example here . So we know the circle and
04:43	we know the distance across the diameter is seven centimetres
04:47	. So this is a fairly common way that you
04:49	think about a circle . If you're thinking about a
04:50	glass or a pot or any circle that you had
04:53	in real life , you probably think about actually how
04:55	big the entire thing was . But if you want
04:58	to work at the area , we don't deal with
05:00	diamonds , we deal with the radius as you can
05:03	see here . So we have to convert our diamond
05:05	are here to the radius . And the radius is
05:07	if you remember , is from the center to the
05:10	edge . This is the entire way across . So
05:12	the diameter is going to be twice that of the
05:15	radius . That is to say that the radius is
05:17	going to equal half of seven , which is going
05:20	to be 3.5 centimeters . So let's go through and
05:24	solve this now . So once again , we're going
05:26	to be using area equals pi r squared pie ,
05:29	which is , you know , I just hit pie
05:30	on my calculator , which is going to be 3.14159
05:34	dot data times 3.5 centimeters times 3.5 centimeters . And
05:41	we just type this into the calculator we hit equals
05:44	and we get our area which is going to be
05:46	38.48 centimeters squared . And that's the way that you
05:53	work out the area of circles . Nothing too bad
05:56	. But it's a really , really important one that
05:58	you get under your belt . If you're gonna be
06:00	OK at maths , okay , It's going to come
06:01	up a fair bit , especially later on . They're
06:03	going to get you doing things like maybe a surface
06:06	area of cylinders or even where later on , if
06:09	you're maybe working out the volume of a sphere or
06:12	the area of a sphere or something like that ,
06:14	It's a pretty handy one to know . Anyway ,
06:16	hopefully you like that video and it was the sub
06:19	. Help to you . Thank you for watching .
06:21	We'll see you next time . Bye .

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