Surface Area of Cone | Math with Mr. J - By Math with Mr. J
Transcript
| 00:0-1 | Welcome to Math with MR . J . In this | |
| 00:05 | video , I'm going to cover how to find the | |
| 00:06 | surface area of a cone . And remember surface area | |
| 00:10 | is the total area of the outside or surface of | |
| 00:14 | a three dimensional shape . When it comes to cones | |
| 00:17 | , we have two surfaces that we're going to find | |
| 00:20 | the area of . And then add those areas together | |
| 00:24 | to get the total surface area . We have the | |
| 00:26 | area of the base and then the lateral area . | |
| 00:29 | The lateral area is the area of the curved surface | |
| 00:33 | , the part that wraps around , so to speak | |
| 00:36 | . So that's our formula , the area of the | |
| 00:38 | base . So this capital B . Right here plus | |
| 00:43 | the lateral area . Now we can make that even | |
| 00:46 | more specific . Will use pi R squared for the | |
| 00:49 | area of the circular base . So pi R squared | |
| 00:53 | plus pi R . S . P I . R | |
| 00:56 | . S is going to give us the lateral area | |
| 00:59 | . Now the R . Stands for radius within that | |
| 01:02 | formula and then the S . Stands for the slant | |
| 01:06 | height . Now I do want to mention that it's | |
| 01:09 | common for an L . To be used to represent | |
| 01:12 | the slant height . It doesn't matter which S . | |
| 01:15 | Or L . They both mean the same thing as | |
| 01:18 | far as slant height for that formula . Before we | |
| 01:22 | go through the example , I want to take a | |
| 01:24 | look at the net of a cone . To better | |
| 01:26 | understand surface area . You can think of a net | |
| 01:30 | as an unfolded three D . Shape . It shows | |
| 01:33 | all of the parts of a three D . Shape | |
| 01:35 | , so to speak . So we have the lateral | |
| 01:38 | area right here and we find that area using pie | |
| 01:44 | times the radius times the slant height and then we | |
| 01:49 | have the base right here which is a circle . | |
| 01:54 | So we use pie times the radius squared . We | |
| 02:00 | add those areas together and we have the surface area | |
| 02:03 | of a cone . So let's jump into our example | |
| 02:06 | here where we have a cone with a base radius | |
| 02:09 | of four inches and then a slant height of 13 | |
| 02:12 | inches . And the first thing that we want to | |
| 02:14 | do is write out our formula . So surface area | |
| 02:19 | equals , we have pi r squared plus pie R | |
| 02:29 | . S . Once we have that we can plug | |
| 02:32 | in our radius and slant height . So surface area | |
| 02:36 | equals kai Radius of four and that is squared plus | |
| 02:46 | pi Times The radius of four Times the slant height | |
| 02:52 | of 13 . And now we're ready to solve . | |
| 02:57 | So at this point you can plug that into a | |
| 03:00 | calculator and either use the pie button or the approximate | |
| 03:04 | rounded version of PIN 3.14 . And whatever comes out | |
| 03:08 | on your calculator will be the surface area of a | |
| 03:11 | cone . Now I'm going to continue simplifying or breaking | |
| 03:14 | this down until I get it in terms of pie | |
| 03:17 | . And then I will calculate the surface area in | |
| 03:20 | decimal form . So let's go through some steps here | |
| 03:23 | in order to do that . And we'll start by | |
| 03:26 | um doing four squared , which is going to give | |
| 03:30 | us 16 . 4 squared means four times four . | |
| 03:34 | So let's put the area of the base in terms | |
| 03:37 | of pie . So we will have 16 times pie | |
| 03:41 | . Now I put the 16 before the pi symbol | |
| 03:45 | there because typically speaking when you have something in terms | |
| 03:48 | of pie , a number times pi you put the | |
| 03:51 | number first plus Well four times 13 is going to | |
| 03:59 | give us 52 . So in terms of pie for | |
| 04:02 | the lateral area we're going to have 52 . Hi | |
| 04:10 | , now we can add our whole numbers together and | |
| 04:13 | combine our pies . So we have surface area equals | |
| 04:18 | 68 pie . And that's our answer . In terms | |
| 04:23 | of pi 68 pi is going to be the surface | |
| 04:26 | area of that cone . Now let's calculate this and | |
| 04:29 | see what 68 pi equals . And I'm going to | |
| 04:33 | use the pie button on a calculator . So if | |
| 04:35 | you're using the approximate or rounded version of pi 3.14 | |
| 04:40 | your answer is going to be slightly different than mine | |
| 04:44 | . So 68 pi equals 213 . And we are | |
| 04:53 | going to round the decimal to the nearest 100th . | |
| 04:57 | So 213 and 63/100 . And this is area so | |
| 05:04 | inches squared . And again I rounded that decimal to | |
| 05:09 | the 100th . So there you have it there is | |
| 05:12 | how you find the surface area of a cone , | |
| 05:15 | find the area of the base and then the lateral | |
| 05:18 | area add those areas together and you have the surface | |
| 05:22 | area . I hope that help . Thanks so much | |
| 05:25 | for watching until next time . Peace . Yeah . | |
| 05:33 | Yeah . Yeah . |
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