Circumference of a circle - math lesson - By tecmath
Transcript
| 00:0-1 | Good day and welcome to the Tech Math channel . | |
| 00:01 | I'm josh in this video . We're going to be | |
| 00:03 | looking at how to work out the circumference of the | |
| 00:05 | circle that is the perimeter , the distance around the | |
| 00:08 | outside of this circle . So we start out with | |
| 00:11 | our circle here and we're just going to label the | |
| 00:13 | major parts of the circle . So we have this | |
| 00:15 | distance from the center here to the edge , this | |
| 00:19 | is the radius or just write that in and we | |
| 00:22 | often give that the letter of our , we also | |
| 00:25 | have this distance here which goes from one end of | |
| 00:27 | the circle to the other edge of the circle going | |
| 00:30 | through the center and this is the diameter . Okay | |
| 00:34 | . And this is going to be often drawn down | |
| 00:36 | as a deep . We also have this distance around | |
| 00:40 | the outside which is what we're going to be working | |
| 00:42 | out , which is the circumference , that is this | |
| 00:45 | distance going right around the outside of our circle here | |
| 00:51 | . Okay . And this is often written as a | |
| 00:54 | C . So now we've got all that . How | |
| 00:57 | do we go about working this distance at this distance | |
| 00:59 | of the circumference ? Well , there's a formula that | |
| 01:02 | quite often gets used and it's this one here . | |
| 01:04 | The circumference is equal to two times pi times are | |
| 01:09 | okay , poem get to in a second . But | |
| 01:11 | this can be rewritten as something even easier . You'll | |
| 01:14 | probably notice that two times the radius here is equal | |
| 01:17 | to the diameter . So this can be rewritten as | |
| 01:20 | a circumference is equal to the diameter times pi . | |
| 01:24 | All right , So what is pi pi is equal | |
| 01:27 | to the circumference divided by the diamond , as you | |
| 01:30 | can see if you rearrange is but it's always 3.1415 | |
| 01:35 | bigger is to say the circumference is always pi times | |
| 01:38 | bigger than the diamond . Now look , you're probably | |
| 01:41 | gonna have a button for pie in your calculator . | |
| 01:43 | But it's around about the following . It's around about | |
| 01:45 | 3.14159 . So what I'm really saying here is that | |
| 01:51 | the circumference of any circle is around about 3.1415 , | |
| 01:56 | 9 times bigger than the distance across that circle . | |
| 01:59 | So , if you want to work out how far | |
| 02:01 | the distance is around , Measure the distance across and | |
| 02:04 | multiply by this 3.14159 . This pie . All right | |
| 02:08 | , so let's try this . Now , for our | |
| 02:11 | first example , we're going to look at a circle | |
| 02:12 | whose diameter is six centimeters and we're going to work | |
| 02:15 | out the circumference . First off , what we're going | |
| 02:18 | to work out is roughly what the circumference is , | |
| 02:20 | and then we're going to work out exactly what the | |
| 02:22 | circumference is . So , roughly what I'd be doing | |
| 02:25 | is I go , okay , we know the diamond | |
| 02:26 | r is equal to six centimeters and pi is equal | |
| 02:29 | to about 3.1 . Force would multiply that by three | |
| 02:33 | and just a little bit three and a bit . | |
| 02:35 | So what is six times three ? And a little | |
| 02:37 | bit you can say okay , this is gonna be | |
| 02:39 | roughly equal to 63 to 18 , so maybe 18 | |
| 02:43 | , maybe a bit in the 19 . So it's | |
| 02:44 | gonna be a little bit over 18 . What is | |
| 02:46 | it going to be exactly ? So if we go | |
| 02:48 | what is six times pi and you'll have pie in | |
| 02:52 | your calculator , this is going to be 3.14159 . | |
| 02:55 | So on and so forth , The more decimal places | |
| 02:58 | you use , the more exact you'll get here , | |
| 03:00 | you would see that this is going to be equal | |
| 03:02 | to 18.85cm . Okay , Roundabouts . And as you | |
| 03:08 | can see here this is between 1819 . We have | |
| 03:11 | a good answer here . It's not a bad idea | |
| 03:13 | with this . Just to give it a bit of | |
| 03:14 | an estimation what it might be first . So that's | |
| 03:17 | the way I go about working out the circumference of | |
| 03:20 | the circumference at distance , around the outside is going | |
| 03:23 | to be 18.85 cm . Okay , what about we | |
| 03:26 | do another one . So for our second example we | |
| 03:29 | have a circle whose radius is four centimeters and we're | |
| 03:33 | going to work out the circumference to do this . | |
| 03:36 | I'm going to first work out the diamond er and | |
| 03:38 | then I'm going to go from there , I'm going | |
| 03:39 | to work out an estimation and then I'm going to | |
| 03:41 | work out the exact amount . So first off , | |
| 03:44 | what is the diamond going to be ? The diamond | |
| 03:46 | is going to be twice that of four centimeters , | |
| 03:48 | So twice a four cm is eight cm . The | |
| 03:53 | circumference then is going to be eight centimeters multiplied by | |
| 03:58 | three and a bit . Three and a little bit | |
| 04:00 | . So what's it going to be ? Well Eight | |
| 04:03 | times three is roughly 24 . So we're gonna expect | |
| 04:05 | an answer above 20 for maybe 25 , maybe 26 | |
| 04:09 | sort of thing . So now let's work out the | |
| 04:12 | circumference exactly . The circumference is going to be equal | |
| 04:16 | to eight times not three and a bit , it's | |
| 04:18 | eight times exact pie , which is pi 3.14159 blah | |
| 04:23 | , blah blah . And that is going to be | |
| 04:25 | equal to 25.13 centimetres . Once again , the more | |
| 04:31 | exact that you use pi , the more exact that | |
| 04:34 | your answer is going to be and sometimes you don't | |
| 04:35 | need exact answers . Sometimes near enough is okay and | |
| 04:39 | sometimes your teacher is going to want you to be | |
| 04:41 | really , really exact , so obviously use it as | |
| 04:43 | much as you need to as you go along here | |
| 04:46 | sooner . I hope you like that explanation on how | |
| 04:48 | to work out the circumference . Once again , depending | |
| 04:51 | on how exact you need to be , you're either | |
| 04:52 | going to be multiplying that diamond by three and a | |
| 04:55 | bit or you're going to be multiplied by pi exactly | |
| 04:58 | 3.1415 Anyway , thank you for watching . If you'd | |
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| 05:11 | the link on screen right now . Also a life | |
| 05:14 | could be nice as well as a comment . We'll | |
| 05:16 | see you next time . Bye . |
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