Volume - the trick to getting it right - Free Educational videos for Students in K-12

Volume - the trick to getting it right - By tecmath

Transcript


00:00	Welcome to the Tech Math channel . What we're going
00:02	to be having a look at this video is we're
00:04	going to be looking at how to work out volume
00:07	. Okay , so The volume is of a solid
00:10	object is pretty much volumes when we're talking about three
00:13	dimensional objects . Okay . Uh , you their dimensions
00:16	, you know , they're objects with 1-3 dimensions are
00:19	length or width and depth . Basically the volume of
00:22	a solid is the amount of space that solid occupies
00:26	. Okay , so the way we measure this is
00:28	in cubic units . So the amount of space ,
00:30	say this particular rectangular prism here occupies . We're gonna
00:34	be looking at how to work at a volume of
00:36	rectangular prisms , such as these also triangular type prisons
00:41	, As you'll see in a little bit . Okay
00:43	, these particular ones like this as well as cylinders
00:47	. Okay . I just want a bit of a
00:49	height . Let's call this 110 cm . We'll get
00:52	back to you . Okay ? So we're gonna be
00:54	looking at how to work out the amount of space
00:56	each of these occupies . Uh so the way that
00:59	we measure the volume of things , we imagine these
01:03	in cubic units . For example this is in centimeters
01:06	. We would measure the volume of these in cubic
01:09	centimeters . And what this is if you can imagine
01:12	a cube and it's a cube , it's a centimeter
01:15	by centimeter by centimeter . Okay so it's one x
01:21	1 by one . Okay . And it's a three
01:25	d little cube . And we would actually write this
01:28	as a centimeters cube . Okay , so just keep
01:33	these in mind because when we're doing two dimensional objects
01:35	, just area we do this in as you remember
01:39	, we got to lengthen a wet we do some
01:41	centimeters squared and we do this distance . Okay ?
01:46	And say centimetres . Okay so this is a difference
01:49	we're doing but this one we're using these particular ones
01:53	. Okay , so let's large straight into this .
01:58	This is fairly easy . And the first thing I
02:00	think you'd want to do with this is make sure
02:02	all your units are the same . Okay , So
02:05	they're all in centimeters . That's good . If they're
02:07	not all in the same unit , change them .
02:09	So they are . The next thing you want to
02:12	do , obviously identify the shape . This is a
02:14	rectangular prison because it's a rectangular box type shape .
02:17	And you apply that sort of rifle . One is
02:19	there's two types of formulas you can use for these
02:22	first one for a rectangular box , like there's a
02:24	rectangular prism . You can use this one where the
02:27	area equals the length times a week , times the
02:32	height of the depth of what you want to call
02:34	it . And that would be centimeters Squared . OK
02:38	. Because there's 1 , 2 , 3 measurements .
02:41	Alternatively , you can also think about it a different
02:43	way where you maybe you work this out about the
02:45	area or the volume here maybe should I be saying
02:50	? Okay , right off the wrong track , I'm
02:51	getting confusing myself . The volume is equal to the
02:56	area . Okay . I see the difference of volumes
02:58	through these shapes . Areas of two dimensional shapes and
03:00	making little mistakes here . Um so if we want
03:04	to know that this particular , say the area of
03:07	this particular base part here , there's 20 x 15
03:11	and we then times is by the height . Occasionally
03:14	if you know the area and you know the height
03:16	, you can just use these , this would give
03:19	us the same sort of thing . So for instance
03:21	, um the area of this particular bottom part ,
03:25	this particular shape here 20 times , 20 times 15
03:31	. Um All right down the bottom here , which
03:33	will also be , you could also call say three
03:38	100 centimetres squared the same . We were given that
03:41	. Okay . Yeah . First off , well consider
03:45	we weren't given this . I'm just gonna do it
03:47	as a standard way . We can go length ,
03:48	times width , times height . Now , the way
03:50	that you can do this is as follows . First
03:53	off . Occasionally , you might be able to read
03:55	this straight off and go , that's this , by
03:56	this , by this and that's fine . But I
03:58	think I've known students in the past get stuck on
04:00	these and what I've recommended you do is this if
04:03	you're you always get these muddled up , which one's
04:06	which and it doesn't really matter when you're doing this
04:08	particular part . But if you are confused about the
04:12	occasionally you get the same thing twice and you're gonna
04:14	end up with 15 times eight times eight which I've
04:16	seen , students do in order not to get confused
04:18	doing this . I would usually go to a corner
04:21	. Okay that's where you go in your 98 .
04:23	But the way you do this is you go to
04:25	the corner of the shape here and you can read
04:28	off each of the dimensions coming off . And so
04:31	this one this one and this one okay . An
04:35	area three different dimensions . So we have 20 centimeters
04:43	times this one 15 celebrators Times This 1 . 8
04:50	cm . Okay with that across a bit running off
04:56	the page . And if we would have multiplied all
04:58	these together , 20 by 15 is 300 times eight
05:05	is 2000 400 centimetres . There's 123 lots of units
05:14	were multiplying in there cube and as we said before
05:17	23 D . Shape . So that makes a lot
05:19	of sense . That's going to be our answer .
05:21	Okay , so 2400 of these little cubes would fit
05:25	into this if they were this one centimeter by one
05:29	centimeter by one centimeter . Okay , the other way
05:32	you can consider this sometimes is so you're already given
05:34	the base , You were given this base colour .
05:38	It is given this base right here And we know
05:43	that it's 300 and on top of that were also
05:46	given were also given it's hard here . Okay ,
05:52	now we're not giving this and we're not giving this
05:56	the way that we can do this is as follows
05:59	. Okay , the volume is equal to the area
06:03	times the height . So we have the volume here
06:06	. We have the area which is This is equal
06:09	to 300 centimetres squared . Tarbes the heart . Right
06:21	centimetres Not square , just eight cm . Okay ,
06:26	so what do we get when we do this ?
06:27	300 Centimeter Square Times . eight . times 8 is
06:32	2400 . And we're going to end up with centimetres
06:38	squared times 10 centimeters . So now we've got centimeters
06:42	cube . Okay , so how did you go with
06:47	that ? All right , okay . Hopefully you get
06:50	this idea that you might be given uh where you
06:53	might be given each one of these and you can
06:55	work it that way , You might be given the
06:56	base and you get the height and you can work
06:58	it out that way . But either way they're going
07:00	to add to the end of the same sort of
07:02	answer . So let's go down to this next particular
07:06	question here was rolled back a bit so we can
07:08	see it . So you were asked to work at
07:10	the volume of this . How would you go about
07:12	this ? Yeah . The way that you go through
07:17	and work out the volume of a um triangular prism
07:22	, like this is as follows . If you want
07:24	to know the area of this triangle here , you
07:28	can work at that and then you could just times
07:30	in that depth there . Are there that height ?
07:34	Okay , because it's the same sort of formula that
07:36	we're using up the volume equals area times height .
07:40	Okay , so I'm going to use that same formula
07:43	, volume equals this area . Times of what we
07:46	have been given the area , We're gonna work this
07:48	out . Okay . It's gonna be the area of
07:51	this particular triangular shape . Yeah . Okay , so
07:59	let's work this out . How would you work this
08:01	out to ? The area of the triangle is as
08:04	follows . Okay , so the area , this triangle
08:07	, I'll get back to this formula for the area
08:10	is going to be half base times height . Okay
08:18	. Which is the area of a triangle , which
08:20	is so the bases , Right ? So half of
08:23	that is four cm times are hard , Which is
08:28	six elements . The area is going to be 4
08:33	, 6 is 24 celebrators squared . Okay , so
08:40	we've got that Area here , which is 24 cinema
08:43	screen or rewrite this out again . The volume equals
08:46	the area . Times are hard . This is going
08:50	to be equal to 24 centimeters squared . Times are
08:58	hard , which is his depth . Now , it's
09:00	going in . Okay . Time six centimeters You might
09:06	say , what do we do this ? 10 cm
09:08	. We don't need this measurement . It's not going
09:10	to help us here . We don't need it .
09:12	Okay , so 24 times six . Do you know
09:17	the answer to that ? It's 144 . 144 centimetres
09:28	shoot . Okay , so you get that idea .
09:33	All right . Um now you might straightaway think ,
09:35	well , why can't we use this particular here ?
09:38	Is our area or this particular back one here .
09:41	The reason is because you sort of need to look
09:43	at this shape and think if I was to keep
09:44	pushing it and it would wouldn't maintain that same sort
09:47	of shape . You know , this one here ,
09:49	all these particular parts here is six centimeters center .
09:53	No matter how much this is going to push all
09:55	the way back to this triangle here . Okay ,
09:59	Another way that you might work this out as you
10:00	might actually work this out , like a rectangle ,
10:02	you might have six length width by height . You
10:05	can actually have it and get the same answer .
10:07	It's a bit of a trick as well . I'm
10:08	not gonna get into that right now . So ,
10:10	what about this particular last one ? Where what we're
10:13	gonna do is we will work out the volume of
10:15	this one . Now the way that we do this
10:18	is really that same sort of formula whether volume is
10:21	equal to the area times the heart , the area
10:25	we're gonna work out , is that circle here and
10:27	then we're gonna have a height . So let's work
10:29	out the area of our circle . So let's do
10:31	this uh area of our circle is equal to what
10:34	the air of circle , it's pie r squared ,
10:38	which is equal to pi Times The Radius , which
10:43	is four Times The Radius , which is four .
10:47	Okay , so what's this going to be all get
10:51	up my calculator . Okay , so we have pie
10:54	which is moving to here ? All right , Times
10:59	four times 4 Equals 50.265 . Okay , so let's
11:06	call this 50.27 . Okay , so this is equal
11:10	to 50 0.27 centimetres squid . Okay , So again
11:21	let's write this formula again , the volume equals area
11:24	times of high and this is equal to the area
11:27	, which is 50.27 ? Celebrate a squared Times The
11:34	height . The height of this is 10 cm .
11:36	This is a nice easy calculation . Okay , 50.27
11:40	centimetres square times 10 is 502.7 . I'm just moving
11:46	the decimal place centimeters cubed . Okay , so hopefully
11:50	you get the idea with this is how to work
11:52	out volume . Okay , so you can either I'll
11:54	move this back up , we'll have a quick look
11:56	at it . You can either go be going length
11:58	times with times height . Okay , And that that
12:01	would be one way that you can work this out
12:03	. So where we're going 20 Okay , because this
12:06	is 20 centimeters uh about 15 cm x 8 7
12:10	. It so you can just go this area times
12:13	height again , This is trying the one . We
12:15	could go this . We went this area types of
12:17	height and saying with these cylinders . Anyway , I
12:20	hope that was the sub help to you . Uh
12:23	, anyway , so next time , Bye .

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