What is Volume in Math? Calculate Volume of Rectangular Prisms & Cubes w/ Units - [5-8-13] - Free Educational videos for Students in K-12 | Lumos Learning

What is Volume in Math? Calculate Volume of Rectangular Prisms & Cubes w/ Units - [5-8-13] - Free Educational videos for Students in k-12


What is Volume in Math? Calculate Volume of Rectangular Prisms & Cubes w/ Units - [5-8-13] - By Math and Science



Transcript
00:00 Hello . Welcome back . The title here is called
00:02 Understanding Volume with pictures and models . This is part
00:06 one . The idea in this lesson is to go
00:09 from the concept of area which we learned in the
00:11 last lesson to talk about one step beyond area which
00:15 is called the volume of an object . So in
00:17 this lesson we're going to concentrate on understanding what volume
00:20 is in terms of pictures and models . And then
00:22 later on we'll learn how to calculate volume . So
00:25 in a nutshell , when you have the volume of
00:27 an object , let's say you're talking about this three
00:30 dimensional object , this is a cube here . We
00:32 want to know how much space this cube occupies .
00:37 How do we figure that out ? Remember for surface
00:39 area let's say we're trying to find the area of
00:41 this board . I would divide the board into little
00:44 squares and so I would count the squares and it
00:46 would be called square square centimeters or square millimeters and
00:50 I would count them up . And that would be
00:51 the area of this flat board . But what do
00:54 I do when I have the volume of an object
00:56 like this , instead of counting squares , I'm going
00:59 to count cubes . It might be tough for you
01:00 to see . But this model has little cubes all
01:03 the way and you can see there's cubes here and
01:05 there's cubes here and you can think of this large
01:07 cube uh as being , how many cubes can I
01:11 fit inside of this thing ? I would count them
01:13 all . And that would tell me how large this
01:16 thing is in terms of of cubic cubic centimeters or
01:20 cubic inches or cubic miles or cubic yards or cubic
01:24 light years or whatever . So instead of square inches
01:27 for volume , we talk about cubic inches for area
01:31 instead of square meters . We talk about in volume
01:34 cubic meters . So it's the same concept . It's
01:36 just that in a flat in a flat sheet to
01:39 find area , we just count squares on the sheet
01:42 . But when we have a three dimensional shape in
01:44 space , how much space does it occupy ? We
01:46 don't count squares . We count cubes . So it's
01:49 called cubic meters or cubic centimeters and so on .
01:52 So let's say for our first problem , we have
01:55 a cube like this and we know that this side
01:58 of the cube is uh well this is really not
02:01 a cube . It's a it's a rectangle . All
02:03 the dimensions are not the same size , but you
02:04 get the idea this side this face of it is
02:06 a cube three centimeters , three centimeters . And the
02:10 depth of the cube are , The depth of the
02:12 object is not quite three . It's a little bit
02:14 shorter in the in the direction of the board ,
02:16 that's two centimeters . How do I measure how much
02:21 space this thing occupies for that ? I'm gonna be
02:23 talking about the volume . All right . So the
02:26 first thing I want you to do is let's just
02:28 look at the bottom layer of this thing . If
02:30 I just cut everything off and look at the bottom
02:31 layer , let's see what that would look like .
02:34 All right . If I slice everything off , noticed
02:36 this is still three centimeters and then going deep into
02:39 the board , it's still two centimeters . Same dimensions
02:42 is what I've had . All I've done is I've
02:43 cut everything away and I've only only looking at the
02:46 bottom layer . I can form a cube here .
02:50 That is one centimeter in each direction and also one
02:53 centimeter deep . We call it a cubic centimeter because
02:57 just like a square centimeter is one centimeter on each
03:00 side . A cubic centimeter is a cube , a
03:03 little bit of cube . Like here , One centimeter
03:05 in depth , one centimeter in width and one centimeter
03:08 in height . One of these things is called a
03:10 cubic centimeter . Just like in my little model here
03:14 , one of these little cubes down here is called
03:16 a would be called in that case a cubic centimeter
03:19 as well . So if I slice it up and
03:21 I have 123 cubes and then 456 cubes , I
03:25 have six cubes on the bottom . So the volume
03:28 of just the slice of the object is 123456 cubic
03:33 centimeters . But the real object is all of that
03:36 plus everything above it . So in order to find
03:39 the volume of the whole object , we have to
03:41 take this six and then we have to count everything
03:43 that's above it as well . Which this is the
03:46 original shape . You can compare this one to this
03:49 one , It's the original shape . But now we
03:50 have sliced cubes into the thing and we knew that
03:53 there were six on the bottom layer . But now
03:56 we have another layer of six and then we have
03:59 another layer of six . So we have six plus
04:02 six more cubes , plus six more cubes . So
04:05 six times 3 . As another way to think about
04:07 that is 18 . So if you wanted to find
04:10 the volume of this thing , the volume V ,
04:13 it's going to be 18 and it's going to be
04:16 cubic centimeters 18 cubic centimeters . Why is it 18
04:23 ? Because what we do is we take the shape
04:25 . We knew that the shape was three centimeters tall
04:27 and three centimeters wide and only two centimeters deep into
04:31 the board . So we know that x centimeter a
04:35 square here , since it's three tall , there has
04:37 to be three of these little squares uh with one
04:40 centimetre each going up and then one centimetre each going
04:43 this way , and one centimetre each going this way
04:45 . So when we take a look at it ,
04:47 we just start by looking at the base and we
04:49 count six of those squares cubes , I'm sorry ,
04:51 six of those cubes . And then we have six
04:53 more , that would be 12 and then six more
04:55 for a total of 18 . So the volume of
04:58 this object is 18 and the unit is not square
05:01 centimeters . The unit for all volume is cubic centimeters
05:05 or cubic meters or cubic millimeters or cubic yards or
05:09 cubic miles or cubic light years . You get the
05:12 idea it's always cubic because we're seeing how much space
05:15 it takes up in a cube , little cubes that
05:17 fit inside . Last thing I will tell you this
05:20 lesson is mostly trying to get you to understand the
05:23 concept 18 cubic centimeters . We can count them and
05:26 we see that there's 18 cubes there but I want
05:28 you to think for a second . Remember that area
05:31 of a sheet is length times with right length times
05:34 with what if I take three times 23 times two
05:39 is six . That's the area of the bottom of
05:42 the cube . When you think about it . I
05:43 mean if this is a cube here and it was
05:45 three times to then then you multiply them . That's
05:47 the area of the bottom three times two or six
05:50 . But if I multiply the six times the three
05:53 here six times three , that's 18 , 18 .
05:56 So the point of this lesson is not to calculate
05:59 the area , I want to count the cubes .
06:01 But I also want to tell you that to find
06:04 the area of a sheet . It's just link times
06:06 with to find the volume of some kind of cube
06:10 or some kind of rectangular shape in three dimensional space
06:13 . We call it a rectangular prism . The way
06:15 you do it is you take length times width ,
06:18 times height , right length , times width , times
06:21 height . So you can do it any order you
06:23 want three times two or 66 times three is 18
06:26 . Let's go in another order three times 3 is
06:27 nine . And then nine times two is also 18
06:30 . So to find the volume of any rectangular solid
06:33 like that . You just do length , times width
06:36 , times height . Now let me go take this
06:38 down and get some more examples so that you can
06:39 get practice . All right , Here's our next problem
06:43 . We have a rectangular solid or also called a
06:45 rectangular prison . That's two millimeters on the bottom by
06:49 two millimeters deep . And then it's in height .
06:52 It's four millimeters tall . How do we find the
06:54 volume ? What we want to do is figure out
06:55 how many cubes fit inside of this . But the
06:58 units are in millimeters , so it's going to be
07:00 cubic millimeters . How many cubes can I fit ?
07:03 Where each cube is one millimeter on an edge .
07:06 How many will fill inside this whole thing . So
07:08 first we take a look at the bottom part .
07:10 The bottom part remember was two millimeters wide and two
07:14 millimeters deep . So if it's two millimeters wide ,
07:17 a cube one millimeter long , I'll fit two of
07:20 them there . And if it's two millimeters deep ,
07:22 I'll fit to one millimeter uh cubes there . So
07:25 you can see how many cubes will I have .
07:26 I have 1234 cubes that are each way . This
07:30 is one millimeter one millimeter one millimeter one millimeter one
07:34 millimeter . So I have four of these cubes which
07:36 are cubic millimeters . So I have four of them
07:39 right here . And then if I look at the
07:40 rest of the shape , I have four of them
07:43 on the bottom layer , four of them here ,
07:45 four of them here and then four of them here
07:47 . So it's 48 12 , 16 . Just count
07:52 them 123456789 10 , 11 , 12 , 13 ,
07:56 14 , 15 or 1314 , 15 , 16 .
08:00 So there's 16 of them . So I would say
08:02 the volume is 16 cubic with millimeters . So that
08:09 means that there are 16 cubes that fit inside of
08:12 the shape where each cube has one millimeter on each
08:15 edge . Now I mentioned to you that to find
08:17 the volume by calculation , you just take the length
08:20 times the width times height . So two times two
08:23 is four . And this four times to , I'm
08:25 sorry , four times two is uh I'm sorry two
08:28 times two is four and then four times four is
08:30 16 . So the formula holds but I want to
08:33 stress in this lesson more how to count them than
08:35 anything else . So let's take this one down and
08:37 do another one . Alright . The next problem we
08:40 have a rectangular solid like this with five m on
08:43 this side and three m tall . And the depth
08:47 into the board is four m . So how do
08:49 we find the volume of this ? We want to
08:51 find out how many cubic metres which are little cubes
08:54 that each have a length of one m on each
08:56 side . How many will fit in this ? So
08:58 let's look First at the bottom layer five and four
09:01 deep . So here again it's five wide and four
09:06 deep . How many cubes are just in that layer
09:08 ? What ? We have ? 12345 m and 1234
09:12 m . So we have , in terms of cubes
09:14 123456789 10 11 12 13 14 15 16 17 18
09:21 1920 . So we have 20 cubes just in the
09:25 bottom layer of this thing . Now let's look at
09:27 the rest of the drawing and see how many more
09:29 we have . We have 20 in the lowest layer
09:32 . So we have 20 cubes in the lower layer
09:35 , 20 more cubes in the middle layer and 20
09:38 more cubes in the top layer . So just like
09:40 counting by twos , 246 you can count by 2020
09:44 . Then there's 40 than their 60 . So there's
09:48 60 cubes in that whole thing . So the volume
09:51 is 60 cubic mhm meters . Mhm 60 cubic meters
09:59 . Now let's see if , by calculating by multiplying
10:01 it works five times four is 20 and then 20
10:05 times 3 2040 60 is 60 . So multiplying length
10:09 times width , times height again also gives us the
10:12 volume will take this down . And we have one
10:14 more left in this lesson . All right , here's
10:16 our last problem of this lesson . We have uh
10:20 rectangular solid , that's uh two centimeters wide , three
10:24 centimeters tall and four centimetres deep into the board .
10:28 How many cubic centimeters are going to fit in ?
10:30 Let's take a look at only the bottom layer .
10:33 So if this was too wide and four deep ,
10:35 there must be uh two cubes each of one centimeter
10:38 here and then 12344 going back each of one centimeter
10:43 . So we have one cube , two cubes ,
10:46 three cubes , four cubes , five cubes , 678
10:49 cubes . So just on the bottom layer we have
10:52 88 cubes noticed . Two times four is eight .
10:55 Okay and then how many layers do we have ?
10:58 So if we have eight here and then ate here
11:00 and then ate here eight times three is what ?
11:03 Eight times three is 24 . So the volume is
11:06 eight times 3 , 24 cubic centimetres , 24 cubic
11:13 centimeters . And also remember that we can also calculated
11:15 by multiplying two times four is eight and then eight
11:18 times three is 24 cubic centimeters . So the point
11:21 of this lesson really was to get you to understand
11:23 what volume is just like area is just counting squares
11:28 in a flat plane and how many squares fit on
11:30 the surface . That's why we call the surface area
11:33 volume is when we have a three dimensional shape .
11:35 How many cubes ? Unit cubes cubic meters cubic centimeters
11:39 will fit inside of an object . and just like
11:42 area to find the area . You multiply length times
11:44 with well to find the volume of a rectangular solid
11:47 like this . You just link times width times height
11:50 , right ? So you just have one more multiplication
11:51 and you get the volume . So in this lesson
11:53 , that's what we covered . I'd like you to
11:55 solve these yourself . Follow me on the part two
11:56 . We'll get a little more practice with understanding volume
11:59 using models .
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