Total Surface Area - the trick to getting it right - Free Educational videos for Students in K-12

Total Surface Area - the trick to getting it right - By tecmath

Transcript


00:00	Welcome to the Tech Math channel . What we're gonna
00:02	be having a look at in this video is how
00:04	to look at the total surface area of shapes .
00:07	Okay , so basically what the total surface air is
00:10	, It's a good over solid say of this shape
00:14	or another shape . We're gonna have to look at
00:15	it . It's basically a combined area of all these
00:18	external outside , uh , surfaces . Okay , So
00:23	we could , we won't have this , say is
00:25	, uh , where we had it is a rectangular
00:27	prism or a triangular prism or even a cylinder or
00:30	something like this . So , but the way that
00:32	you work them out is fairly similar each time .
00:35	So the steps that you do when you want to
00:37	work at the total surface area are as follows first
00:41	. Pretty much what you have to do is you
00:42	have to find the area of each face . Okay
00:46	, so the way I typically do this safely shape
00:49	as this is , I did this a little bit
00:53	unconventionally . I think people tend to do this nice
00:55	working out here and number things . I actually tend
00:58	to do this . I tend to have a lot
01:00	of arrows when I do this and have So I'm
01:03	pointing at this shape here . Okay , so first
01:07	off , what is the area of this shape here
01:11	? Okay , so we have lengthier Which is 20
01:15	cm . We have I with here of this particular
01:23	rectangle here , Which is the same as this 1
01:26	. 15 celebrators . Okay , because the area is
01:30	length times with so what we're gonna do here is
01:34	we multiply these guys together , so 20 times 15
01:38	is 300 centimetres squid . Okay , now the next
01:46	one we're gonna be having to look at is say
01:48	we choose a different one . We're not going to
01:49	choose this one because this one is identical to this
01:51	. I'm going to choose one or the other side
01:53	. Say I'll choose this one . Yeah . Okay
01:58	. And the way we work , this is another
02:00	rectangle . Okay . But it's looking a bit of
02:03	a slant . So this is also going to be
02:05	an area equals length times width . So we got
02:07	the length which is going to be I say eight
02:11	cm And this is going to bother with which is
02:16	15 cm . So what do we get ? We
02:22	multiply these two guys together 15 times eight is 120
02:27	cm squared . Okay , And the next one I
02:32	get now is I'm going to be looking not this
02:36	one . Not this one . Can you spot the
02:38	way we're looking at ? We're going to be looking
02:40	at this one . Right ? Yeah . Okay .
02:45	And if you're really uncertain and which ones you already
02:48	worked out ? The way you might do it Is
02:49	this you might go to the corner of your shape
02:52	and you're going to be doing this one here .
02:55	Okay , This one in the corner . Okay ,
02:58	so we've got this one here , we've done this
03:00	one in the corner and now we're going to be
03:01	looking at this one in the corner . Okay ,
03:05	So the way that we do this is as far
03:07	as it's another rectangle , gonna do length times with
03:10	, which is the same as the length , which
03:11	is 20 centimetres . And we're gonna be multiplying this
03:16	by this high tea or which is going to be
03:19	8cm . And what we get is we get 20
03:24	times eight and we get 160 centimetres squared . Their
03:31	first off , we're going through we were multiplied all
03:33	these and now we can go to well , there's
03:35	also a number of other sides that we have to
03:37	work out . We get to work out this side
03:39	here . But what we might realize is that this
03:41	side here is the same as this side over here
03:43	. Okay , So we're gonna get this answer here
03:46	. And we're going to multiply by two . We
03:48	have a similar side to this side here , It's
03:52	dead . Are you okay ? We're gonna be multiplying
03:55	this point to we're going to have a similar side
04:00	to this front side , which is this backside here
04:03	. So we're gonna multiply this one too . So
04:05	we got on each of our boxes here , we've
04:07	got a complimentary side on the other side , which
04:09	is exactly the same area . And then what we're
04:11	gonna do is going to multiply this by to sort
04:13	through that right now and I'll put them underneath .
04:16	So 300 times to 300 centimeters square by two is
04:20	600 celebrate a sweat . We have 120 times two
04:28	, which is 200 40 centimeters squared . And then
04:34	we have 100 and 60 centimeters squared by two which
04:37	is 320 centrally to swear . And finally what we
04:42	have to do is because it's the total surface ,
04:44	everyone of the total of these guys are together ,
04:46	we're going to add all these together . So 600
04:50	Plus 240 Plus 320 . If we add all these
04:55	up together , you get the answer , oh ,
04:59	1160 centimetres squared . Okay , so just a couple
05:08	of things to recap on that one . Again ,
05:09	when you get these sort of questions , I tend
05:11	to , yeah , it's good to go to a
05:13	corner and you might get this one in the corner
05:16	, this one in the corner and this one of
05:17	the corners so that each , each particular uh ,
05:22	part of the quarter there and then you also will
05:24	be working . So you work at the area .
05:26	Those need to work at the area on the other
05:27	side . You just multiplying by two . Okay .
05:30	So we worked at all those that we add them
05:33	all together . Okay , because it's a total service
05:35	here is a look at the service area one ,
05:37	2 , 3 , double it then out of together
05:42	. Um So that's nice and easy . That's a
05:44	fairly uh simple thing to do . What about we
05:47	have a look at a bit more of a people
05:49	are complicated shape , which is this one here .
05:52	Now look , I really recommend with obviously when you're
05:55	doing these , look at the shape we've got ,
05:56	you might think well how am I going to solve
05:58	this ? This is a triangular solid . And what
06:01	you're gonna realize that has the same triangle here ,
06:03	front and back . So we can work that out
06:05	. The triangle out and double it . But we
06:07	have an individual side here that's not replicated twice .
06:10	We have this an individual side on the bottom here
06:13	and this diet and all side is also different .
06:15	There are three different rectangles on each side of this
06:18	, the non faith sides . So let's have a
06:22	look at this . Let's first work out the area
06:25	of these tribals . Okay , so I put an
06:29	arrow going there . You might , you know ,
06:32	it's very easy to get maybe confused of what ,
06:35	Which ones I'm looking at . So I'm looking at
06:37	this particular triangle here . Okay , so what's the
06:43	area of a triangle ? It's area for a triangle
06:48	is half the base times are hard , which is
06:53	equal to This triangle here , we have a base
06:57	here which is eight cm so half of that is
07:00	four centimeters top of the heart , which is six
07:05	centimeters . So four centimeters time six centimeters is 24
07:10	centimeters squid . Okay , now there's two lots of
07:15	these . There's 12 straight away . I can double
07:19	this so times two and that equals all right here
07:25	in different colors . So it shows up . I'll
07:27	put it in . Red is 48 centimetres squared .
07:33	Ok , So we worked out the area of our
07:35	two triangles . Okay , the next thing we do
07:41	is we have three rectangles . We're gonna work out
07:44	. Okay , So we've got this rectangle uh here
07:50	we've got this rectangle which is going to be on
07:52	the bottom . Which is Yeah . And we've also
07:55	got this rectangle at the back which is here .
07:59	Okay , so let's work these out . Okay ,
08:03	so first off , we have this particular triangle here
08:06	. This diet only shaped triangle which the area is
08:09	length times width , so which is six by 10
08:12	centimetres , six centimeters by 10 centimeters . Which is
08:19	equal to Remember red as well , 60 cm squared
08:26	. We have Now we have this bottom one here
08:30	which is another rectangle which is eight bye six celebrators
08:36	, eight centimeters time . Six celebrators , which was
08:40	able to six sites are 48 celebrators squared . And
08:48	finally we have this back rectangle here , which is
08:52	six x 6-6 cm by six centimeters , Which equals
08:59	six . Sixes 36 centimeters square . Okay , so
09:06	now what we have to do to work out the
09:07	total surface area is we're going to add All of
09:12	our different areas together . 48 x 60 plus 48
09:17	plus 36 . And if you add all these together
09:20	, what answer do you get ? Get this answer
09:23	of 100 authority to centimetres squared . So that's how
09:31	you work at the total surface area . How did
09:34	you go with that ? What about what was going
09:36	to ? But I might add just one more to
09:38	this . What about if we do um this particular
09:42	shape ? So I'm going to have to do this
09:43	bit of a shape on the fly . Okay ,
09:45	so let's have a look . It's going to be
09:48	this sort of shape . What about it ? We
09:50	have we'll see how this goes . You don't shape
09:56	? I'm gonna draw here . So we have uh
10:00	he soda . Okay , so there's a cylinder .
10:08	All right . So we'll say working at the total
10:11	surface area of a cylinder , it's going to be
10:12	slightly different , isn't it ? But what you might
10:14	realize is this it's a bit more tricky now ,
10:19	But you have a couple of different shapes here .
10:22	So , first off , I put some dimensions on
10:24	the types of dimensions we need , all we really
10:26	need for this is we need a height . So
10:28	say I'll make this a nice easy . Hi ,
10:30	I'm going to make it 10 cm and I'm going
10:32	to make this don't have it here . The whole
10:36	way across . Actually . I'll be I won't be
10:38	that cute old is called the radius here . The
10:40	radius is the halfway point and I'll call the radius
10:43	from here to here . That's cool . Say something
10:46	small like Two cm and no , really not to
10:50	scale there . I did that typical math teacher think
10:52	of drawing a line . It's totally not the scale
10:54	. It's obviously not two cm . That's 10 .
10:57	Okay . In fact , it's gonna bother me that
10:59	much . I'm gonna fix it up and make it
11:01	into . It's caught . Let's call it four cm
11:06	. Okay . Yeah . All right . So how
11:10	would you go about working at the total surface area
11:12	of this ? Now , what you might realize is
11:14	we have a circle at the top circle at the
11:16	bottom . And we also have this way this rectangular
11:20	shape . We were to get this in an open
11:22	this up . We would end up with a rectangular
11:24	shape . You might get that if we were to
11:25	. So you get a toilet , if you're not
11:27	sure this , get a toilet roll and cut it
11:29	along one edge and undo it and see what you
11:31	get , you're gonna get this nice rectangular shape ,
11:34	The length , which is gonna be the distance all
11:36	around this circle and the width , or the height
11:39	here , which is going to be is hot .
11:41	Here's ted okay , there's a couple of things we
11:44	have to work out , we have to work out
11:45	the air of our circles . And also we have
11:47	to work out this length here is going to be
11:50	okay , So let's do that . So first off
11:54	, uh well let's let's work at the circles on
11:56	top , so if we don't do that , draw
11:59	a circle . So that's what we know . We're
12:00	working out the way that we would do this is
12:03	this is equal to pi of Squared because there's two
12:08	of them a lot of times that answer by two
12:11	. So if we do this right now , let's
12:15	have a look at our particular answer . I'm gonna
12:17	pull the calculator because we use the pie . So
12:20	I'll put this calculated up here and I'll use it
12:23	the second and we'll what we'll do is we'll modify
12:26	some numbers in . So first off , what we're
12:27	gonna do is get pi r squared . Pie is
12:30	a pie , The radius is four square , that's
12:36	at four times 4 times two . And if we
12:40	would do this we're going to get the answer here
12:43	of I'll do this right now , Clear this other
12:47	number up . We got pie Times four times 4
12:53	times two And this is equal to 100 53 I'm
12:59	just gonna call it 100.5 , I think that will
13:01	suffice . So 100 point five centimeters squared and that's
13:09	for both the top and the bottom because we doubled
13:11	it by times a year by two . Okay ,
13:15	uh so now what we got there , there are
13:17	two circles , we're also going to work out the
13:19	area of our particular uh this this particular rectangle shape
13:25	. If we were to get this this part here
13:27	and chop it here and undo it would end up
13:29	with this shape , there was a rectangle , There
13:32	was 10 cm high , but this would be equal
13:36	to the circumference of our circle . Okay , so
13:39	first off let's work out what this circumference is .
13:42	Okay , so the circumference of the circle , we
13:44	can work out as follows , The circumference is equal
13:48	to two part oh so this is equal to two
13:56	times pi times for so let's work out what this
14:00	is . Okay , I'll move the calculator here ,
14:03	clear that up two times pi times four 25 .13
14:13	. So let's call it 20 5.1 centimetres . So
14:19	what we're left with is we're left with a rectangle
14:24	where the circumference is now going to be 25 0.1
14:30	. So the area , this particular shape , he's
14:32	going to be all right . The formula here ,
14:35	area equals length times width because the direct angle and
14:39	we've now worked out the length and the width we
14:41	got this is basically the length we're gonna call this
14:46	20 call is 10 cm and this is going to
14:50	be times 25 0.1 centimeters , Which is going to
14:57	be equal to The way you can probably see it
15:00	, throw it away . 251 cm squared . So
15:06	total surface area , total surface area you say It's
15:11	always very easy with these to lose plot of what
15:13	you're doing . We're going to add these guys together
15:16	. So 100.5 here and we're gonna add this to
15:19	251 . Okay , I'll write that one down 100
15:24	.5 cm two . Class 251 cm Squared . And
15:33	answer is going to be I would be saying 351
15:39	0.5 centimetres squared . So how did you go with
15:44	those ? Okay . That was just meant to show
15:46	you how to work them out . Look , I
15:47	seriously reckon sitting down and learning formulas for these except
15:51	for the ones of how you would work out ,
15:53	you know , a circle or a square or a
15:55	rectangle or triangle . I don't think going beyond that
15:59	for working at total surface area . Big long strings
16:01	are formally as you can get . I don't think
16:04	that overly useful a lot of time . I think
16:05	it's a lot better to try and actually break it
16:07	down yourself and trying to do it that way .
16:09	I think conceptual you'll feel a lot better about what
16:11	you're doing rather than just coming out with this seemingly
16:14	very random numbers . Anyway . I hope that was
16:17	a some help . Well , we'll see you next
16:19	time . Okay , bye .

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