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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