Area of circles - Free Educational videos for Students in K-12

Area of circles - By tecmath

Transcript


00:00	Good day and welcome to the Tech Math channel .
00:02	What we're gonna be having to look at in this
00:03	video is how to work out the area of circles
00:06	. Okay , so , uh , this is ,
00:08	uh , the amount of space I guess enclosed by
00:12	a circle . And so the way that we do
00:15	this is as follows , I'll draw a circle and
00:18	I think first off , I'll just go through a
00:19	few of the terms that will be using when we
00:22	are looking at the area of circles . First off
00:25	, we're gonna be looking at this thing called the
00:27	radius . The radius is the distance from the middle
00:31	, the edge , which is the same . No
00:32	matter where you are . Okay , So this is
00:35	called the radius from radius . And the other way
00:42	we might measure a circle , as you say ,
00:44	in terms of this entire distance across which is called
00:49	the dye amateur . Now the diamond are , as
00:53	you probably can see here is twice that of the
00:56	radius . Now , the way that you work out
00:58	the area of a circle is as follows . The
01:03	area of a circle . People's part uh squared .
01:08	Pie is a special constant . That's used to work
01:11	out circles arm . Generally It's equal to about 3.1415
01:17	. But the easiest way and the most accurate way
01:19	for you guys to use it is to actually get
01:22	the calculator , we're gonna be multiplying that by the
01:25	radius squared by the radius , times itself . So
01:28	whatever this is time itself . What the calculator are
01:33	off the computer . As you see , I've actually
01:37	got a put from standard mode into scientific mode and
01:42	We got down here pie . Okay , it's not
01:44	on a lot of calculators will be written like this
01:46	, but on this particular one it's written as pie
01:49	. And if we do that , uh we actually
01:51	end up with a really big long number . Okay
01:53	, 3.14159265 Blah Blah Blah Blah Blah Blah , Blah
01:57	Blah Blah . Because big a rational string of numbers
02:02	. So we're gonna use this to actually work out
02:05	the air of a circle . That's pretty easy stuff
02:08	. Sorry . These are the types of questions you'll
02:10	get when you get asked to work at the arab
02:11	circle . So I'm gonna leave that particular formula there
02:16	because we're gonna be using our lot . Let's tell
02:18	you , we have the circle here and we wanted
02:20	to work it out and the radius here , we
02:23	wanted to work in the area , the radius we
02:26	know to be uh Get rid of that . The
02:30	radius is five cm . The area is what we
02:35	want to know the area . Obviously the space within
02:38	here , we're gonna be working out in centimeters squared
02:42	games where the radius and centimeters are and is going
02:45	to come out in centimeters squared . So first off
02:47	, what we do is we're just going to sub
02:49	in this formula . So this equals two pi Times
02:52	Radius Square , which is five Centim times five cm
02:59	. And now it is going to hit this into
03:01	our calculator . Okay , so first off , let's
03:06	go pi times five times five . And we get
03:10	the answer of 78 .54 rounded up 78.54 cm squared
03:22	. That's how easy it is to work out the
03:24	area of a circle . But it's really , really
03:26	critical that you remember this particular formula here . Okay
03:32	, so what about we go , another one of
03:35	these and what about you give it a go for
03:38	working out to say you have I'll give you a
03:41	one with a diamond at this time . Remember diameter
03:43	is twice that of the rate is twice the size
03:46	of the radio . So I'll draw a circle and
03:49	the one I want you to work out as a
03:52	diameter all the way across of what ? About 18
04:00	laters . Okay . So what we're gonna do is
04:04	going to work in the area , That area equals
04:06	pi r squared . So this sequence pie . So
04:08	you might work this out there pauses and then I'll
04:11	come back and answer it . You pause it .
04:13	Anyway , I'll answer it now , Times The radius
04:15	. The radius is half the diamonds sometimes nine tom's
04:19	doing . And these are both in meters . So
04:22	the answer is gonna be a meters squared . Okay
04:26	, I can fix it up right now . Just
04:28	uh nine m times nine m . So the area
04:34	to this eagles as follows . Let's get the calculator
04:37	up . Clear that . So pi Times nine times
04:41	9 It was 254.47 . What was that ? 254
04:49	.47 . I hope that the double shape that 254.47
04:54	, correct . Okay . And that's in meters squared
04:59	. That's how easy it is to work at the
05:01	area of a circle . Now , the other type
05:03	of thing you might get asked this of course ,
05:05	is you might get asked where it's actually a segment
05:08	of the circle . Um to say you were given
05:11	a circle life as follows . I'm not going to
05:14	go half a circle . That's what you're expecting .
05:16	Say you actually were asked to work in the area
05:19	. Uh huh . This quarter circle and what you
05:24	knew is only one thing , which is this distance
05:26	here , which is 6cm . So in the area
05:32	of this this is a half . This is a
05:36	1/4 circle . Okay . That might not be a
05:38	very good picture of one , but it's a quarter
05:41	to the area equals hi squared because it's a quarter
05:47	of a circle which wants to draw , it would
05:51	look like this is a circle that's a quarter of
05:54	it . We're gonna actually divide our answer , Boy
05:58	four . Okay , so let's do this . Uh
06:07	So this equals pi Times the radius which is 6cm
06:13	Time six cm squared , divided by four . And
06:17	we're just going to go in the order . It
06:19	is red . So let's just get our calculator out
06:22	. We're gonna go pie Times six times 6 times
06:29	Clear , started again five times 6 times six divided
06:36	by four . It was 28.27 . Okay , so
06:41	this equals 28 0.27 centimetres squared . Now I just
06:50	wanna put this calculator up just to show you something
06:53	really , really quickly with this and this is this
06:56	. So you decide , okay , I'm not gonna
06:58	use pie instead pies around about as you see 3.14159
07:03	instead , what you're gonna use is 3.14 Because this
07:06	is the type of problems you get with this ,
07:08	I'll show you the difference that you get if you
07:10	use pie or if you actually use this particular number
07:14	here , it won't seem like much soap I three
07:18	instead of pie . We're using 3.14 times six time
07:22	six Equals divided by four equals 28.26 . Now You
07:30	say that's not actually much of a difference and it's
07:32	not in the scheme of things , it's possibly not
07:34	a huge difference . So this is if we use
07:36	3.14 , we get 28.26 . Just double check that
07:42	that's what we got centimeters squared . Yeah , that's
07:46	only 1/100 of uh it's 100th of a centimeter square
07:52	. It's not a huge amount . Just be wary
07:53	with certain applications . We really , really want to
07:58	have this exact . In fact , I think it's
08:00	really , really good policy that you shouldn't get this
08:02	as an answer . I know it's very pedantic ,
08:05	but you should be using pie . The pie button
08:08	. Okay . I know some calculators don't have pie
08:11	, so yeah , you're sort of stuck there .
08:13	Okay , But try to get one that has pie
08:16	anyway . That's how you can go working at the
08:18	area of circles , possibly our quarter circles . Okay
08:22	. See you next time .

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