Three-Dimensional Figures - By Anywhere Math
Transcript
00:0-1 | Welcome anywhere , matt . I'm Jeff Jacobson . And | |
00:03 | today we're gonna talk about three dimensional figures . Go | |
00:10 | , let's get started . Alright , for today's lesson | |
00:31 | , there's gonna be a lot of terms and a | |
00:33 | lot of pictures and drawings to make . So make | |
00:36 | sure you take really , really good notes . Okay | |
00:39 | , so today we're talking about three dimensional figures and | |
00:42 | before we get to any examples , there's quite a | |
00:44 | lot of terms and vocabulary words that we need to | |
00:47 | talk about . So first , if I look at | |
00:51 | all of these , well what are they we call | |
00:54 | them ? Solid and solids are three dimensional figures that | |
01:00 | take up space . You've got a cube , pyramid | |
01:04 | , triangular prism . Uh We got a cylinder , | |
01:08 | a cone and a sphere . They're all solid . | |
01:12 | Some of these look like they might belong together . | |
01:15 | And some of them don't . Okay . The next | |
01:19 | word , we're going to talk about our poly Hadrian's | |
01:22 | . Well , which ones of these are poly hydrants | |
01:25 | . Holly hydrants are three dimensional figures , right ? | |
01:30 | But all of the faces are polygons . So that | |
01:34 | means if there's anything that looks rounded like a sphere | |
01:38 | , it's not a poly hedren . So this doesn't | |
01:40 | work . Uh cylinder is also not a poly hedren | |
01:44 | comb . Not a poly hedren . Right ? It's | |
01:47 | rounded on this part here . At the base is | |
01:50 | a circle . That doesn't work . But these ones | |
01:53 | left over . Yes . Pyramid is definitely apology . | |
01:56 | Adrian cube for sure , triangular prism . Those are | |
01:59 | all Polly Hadrian's . All of these faces are polygons | |
02:05 | . Okay . Next we're gonna take a look at | |
02:07 | a cube and talk a little bit more about some | |
02:10 | more vocabulary words to describe this cube . First word | |
02:14 | we're going to talk about is face . Well what | |
02:17 | is a face on a on a poly hedren ? | |
02:20 | We're not talking about a face like this . Faces | |
02:22 | like a side of a poly hedren or a three | |
02:26 | D . Figure . So if you look at this | |
02:28 | cube , how many faces does it have ? Well | |
02:31 | we've got the front and the back . That's too | |
02:34 | we've got the left and the right . That's two | |
02:37 | more . So that's four and we've got the top | |
02:39 | and the bottom . So all together this has six | |
02:42 | faces . Next let's talk about this part . Right | |
02:46 | here we call this an edge and edges where two | |
02:51 | faces meet . That's all it is . So we've | |
02:54 | got an edge here where this facing this face meat | |
02:58 | edge right here with this face in this face meat | |
03:01 | . So if we look at this cube , how | |
03:02 | many edges does it have ? Well we've got 1234 | |
03:09 | 5678 and on the bottom 9 10 11 12 12 | |
03:16 | edges in this Cube . Next word we're going to | |
03:19 | talk about is right here that's called the vertex And | |
03:24 | a vertex is where three edges meet . So right | |
03:29 | here this vertex there's an edge . An edge and | |
03:32 | an edge where they meet that's called a vertex . | |
03:36 | Well , how many virtues is that's plural for vertex | |
03:40 | does this cube have ? So let's see , we've | |
03:42 | got one here . 234 And then on the bottom | |
03:47 | 56788 vortices . Here's one to shine your own . | |
04:01 | Next . We're going to talk about a couple of | |
04:03 | very common polly hydrants and the first is in prison | |
04:08 | . Okay . A prism is a poly hadron that | |
04:12 | has two identical parallel basis . And we're not talking | |
04:18 | about base like two dimensional . Like when you find | |
04:21 | the area of a parallelogram and its base times height | |
04:25 | . We're talking about uh sides or faces as the | |
04:29 | basis . So for example , this is a prism | |
04:34 | . It is a triangular prism . And the reason | |
04:36 | it's a triangular prism is because the basis are triangles | |
04:41 | . You name the prism after the base . So | |
04:44 | right here there's a triangle . Here's another identical triangle | |
04:49 | and they are both parallel with each other , which | |
04:53 | is why it's called the triangular prism . The way | |
04:56 | I like to think of prisms as think of the | |
04:59 | base as whatever shape is being stretched . Okay , | |
05:04 | so it's like we've got a triangle here and I | |
05:07 | take that triangle and I stretch it out to make | |
05:09 | a prism . Now one other thing to know about | |
05:13 | prisms is that these faces in between the basis are | |
05:21 | always going to be parallelogram and we call them lateral | |
05:25 | faces . Okay , so these these faces in between | |
05:30 | the bases are lateral faces . So here's a triangular | |
05:34 | prism . Uh Here's another example of a triangular prism | |
05:39 | , right ? It's smaller but same thing you've got | |
05:42 | a triangle and you're stretching it out to make a | |
05:44 | prism . Uh Here you can call this a square | |
05:48 | prism . Here's a square , an identical square that's | |
05:51 | parallel another prism . And notice the lateral faces are | |
05:55 | still parallelogram . They're rectangles but rectangles are parallelogram . | |
05:59 | So that's okay , these are prisms . The next | |
06:03 | Paula , Hedren we're going to talk about is a | |
06:05 | pyramid . Now , I'm sure all of you know | |
06:07 | , pyramids , you know , like the pyramids in | |
06:09 | Egypt and stuff . But let's get technical about it | |
06:12 | . A pyramid unlike a prism only has one base | |
06:17 | . So this base is a square , which means | |
06:21 | we call this a square pyramid if you had a | |
06:25 | pyramid like this ? Well , the base here is | |
06:31 | a triangle . So this is not a square pyramid | |
06:34 | . It's a triangular pyramid . So , you name | |
06:38 | the pyramid after whatever shape the basis . Okay , | |
06:43 | now , if we look at these pyramids , the | |
06:45 | lateral faces , these here and here , they are | |
06:50 | not parallel , ingram's like they are in prisons instead | |
06:53 | . They're always gonna be triangles . Okay , so | |
06:57 | here are pyramids . Ok , I was able to | |
07:00 | draw a rectangular prism . Now it's a rectangular prism | |
07:04 | , which means the basis need to be rectangles . | |
07:08 | So to draw you need two identical rectangles . So | |
07:12 | I'm gonna start with the first one . Next step | |
07:14 | , you just go up and over a little bit | |
07:17 | to draw your second and try to make it identical | |
07:20 | to this at this point . All you need to | |
07:22 | do is connect the corresponding angles . So top left | |
07:27 | , I connect with top left , like that , | |
07:30 | bottom left with bottom left , top right with top | |
07:34 | right and bottom right with bottom right . So now | |
07:40 | you can start to see it looks three D . | |
07:42 | Like a rectangular prism . Last thing is you have | |
07:45 | to make the the lines that you can't see . | |
07:48 | We call those the hidden lines , you make those | |
07:51 | dashed . So this is where you need a pencil | |
07:53 | . So I'm just gonna erase that's going to be | |
07:57 | a hidden line because I wouldn't be able to see | |
07:59 | it looking at the prison from the front that would | |
08:03 | also be hidden . And so would that one . | |
08:09 | So that is the rectangular prism . Let's try one | |
08:13 | more . Okay , part be dry triangular pyramid , | |
08:18 | triangular pyramid means that base is going to be a | |
08:21 | triangle . So I'm going to start with that and | |
08:23 | then remember all of the , all of the sides | |
08:25 | come up to a point come up to a vertex | |
08:28 | . So you put a point up here and just | |
08:30 | simply connect each of those uh vertex is up to | |
08:37 | that point like that . And then you gotta make | |
08:40 | your hidden line . So I'm gonna make it as | |
08:42 | this this face here is going to be the front | |
08:44 | . So these are gonna be all hidden . Okay | |
08:54 | ? And that is your triangular pyramid . Now real | |
08:56 | quick . If you wanted to do a square pyramid | |
09:00 | , you gotta be careful because if you do the | |
09:03 | same technique and draw a square point and then up | |
09:07 | here you're gonna look at that and say that looks | |
09:12 | really weird . Right ? Well the trick is to | |
09:15 | not draw a square , make it look more like | |
09:18 | a parallelogram kind of slanted . So if you draw | |
09:23 | it like that then you put your point up there | |
09:26 | if you want to go over a little bit so | |
09:28 | I can see that that line and that line are | |
09:30 | different , connect those , connect those and then make | |
09:36 | your hidden lines . Hopefully that looks a little better | |
09:41 | . Right ? That definitely looks better than the other | |
09:42 | one . Let's try one more example , our here's | |
09:45 | our last example , draw the front side and top | |
09:48 | views of the solid . So we're gonna do this | |
09:51 | triangular prism . So the front view is if it's | |
09:55 | sitting like this , what does it look like coming | |
09:57 | from the front ? Well when we're drawing these views | |
10:00 | you can't see three D . So when we draw | |
10:04 | it it's just gonna be a two D . Shape | |
10:06 | . So from the front all you see is you | |
10:08 | see this bottom line and that top and then it | |
10:12 | just looks like a straight line coming down . We | |
10:14 | can't draw angle like we know it is it's just | |
10:17 | coming straight down . So a front view , make | |
10:21 | sure you label each of these Front view would look | |
10:24 | just like a thank you . There's my front view | |
10:28 | next the side view again . Well that would be | |
10:31 | coming from the side . Well we know the side | |
10:35 | of this triangular prism is a triangle here , that's | |
10:38 | one of those bases . So side view is just | |
10:41 | a little triangle . And keep in mind these heights | |
10:47 | here should be the same , right ? Okay . | |
10:50 | Uh so keep that in mind when you're making your | |
10:52 | drawing , it wouldn't make sense to draw a huge | |
10:54 | triangle if that was my front view . And finally | |
10:57 | the top . What does it look like when you | |
10:59 | look at this figure from the very top straight down | |
11:03 | ? So if I turn it and you look well | |
11:06 | it's gonna look like a rectangle with this line right | |
11:10 | in the middle , okay , for that top edge | |
11:13 | . So that's your top you so you're gonna have | |
11:17 | another rectangle but that's going to have that line going | |
11:22 | right through the middle . Here's some more to try | |
11:25 | on your own as always . Thank you so much | |
11:34 | for watching . And if you like this video , | |
11:35 | please subscribe . |
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