Surface Area Half Cylinders - Free Educational videos for Students in K-12

Surface Area Half Cylinders - By tecmath

Transcript


00:0-1	Good day and welcome to Tech Math Channel . What
00:02	are we having a look at in ? This video
00:03	is going to be looking at how to work out
00:05	the area of the surface area of half cylinders .
00:08	Okay , this special video , my nephew has asked
00:11	for a bit of help with this for his homework
00:13	. So I'm sending this out to you . So
00:16	, um anyway , the type of the question I
00:19	I think you're asking me to answer is this type
00:21	of one where what we have is we would have
00:24	a cylinder here , which I've got here and we're
00:27	looking at working out this surface area . A half
00:32	a cylinder . Okay , so I'm going to draw
00:34	this in as best as I can , sort of
00:36	three D . J . Okay , so we're going
00:37	to end up with something looks a bit like this
00:40	. A half circle of Yeah , and this is
00:42	going to go down to yeah , this is going
00:45	to go down to uh I'm gonna end up with
00:49	a line here and I'm also going to end up
00:52	with this type of thing where I'm going to end
00:55	up with this cylinder part . So we're sort of
00:56	going to see We got a couple of different parts
00:59	of Yeah , we've got these two half circles on
01:02	top of the bottom . We got this rectangular part
01:04	here . I don't know whether you want this included
01:06	or not , and we have this half arm cylinder
01:08	part on the other side . Okay , so let's
01:11	work out a different part of these . So ,
01:13	first , I'll give a bit of an arbitrary sort
01:16	of height and radius with because that's the two measurements
01:19	when the need . We're gonna need a radius .
01:21	So I'm gonna give one , say as two and
01:23	a height as let's call it five . These commands
01:27	, centimeters meters , whatever . Okay , so ,
01:30	first off , what about we We basically were number
01:35	Our side . So , yeah , we're going to
01:36	have this side here . This one . We're gonna
01:38	have this side here , which is to this this
01:40	rectangular side we're gonna have this is three . This
01:42	bottom one which is going to be the identical number
01:44	one here and four . Okay . Which is going
01:46	to be a semi circular part ? I asked semi
01:49	cylinder part . Okay , so first off , let's
01:52	work out the Surface area of # one party .
01:56	Okay , number one is a half circle . Okay
02:01	, So number one , the way we're going to
02:02	work out the area of a circle is as follows
02:05	, we use this formula as you probably well know
02:07	which is pi uh squared . Ok . So this
02:11	is equal to five times are times are all right
02:15	? All right , that down it's a sequel to
02:17	pie . Uh huh . And this will be as
02:23	follows . Okay , um actually get a calculator up
02:25	more will use this . So here's my calculator .
02:28	Um And you're going to see that we have Hi
02:33	Which is going to be pie ? Well he got
02:36	up in the second and the radius which is to
02:41	by two . Okay and then you know what we're
02:44	gonna do ? We're gonna have it . Okay so
02:45	so I do remember this . Okay so we're gonna
02:47	go for this will go pie which is down there
02:51	pie times two times . So And this is equal
02:58	to 12.56 but we actually want half a circle .
03:02	Okay ? But actually I'll tell you what well this
03:06	is um you're gonna probably realize that number three down
03:09	here is also gonna be that same size to rather
03:10	than harvey and I'm just gonna keep a whole circle
03:12	here . Okay do you get what I've just done
03:14	there rather than having this answer right now ? This
03:17	No one , part Oh yeah , I'm actually gonna
03:20	not have it but I'm going to include it as
03:22	number three here . Okay . So what I'm gonna
03:26	do with this answer this 12.56 . I'll just put
03:29	it in the memory here . Memory pass . Okay
03:32	, So let's clear now . And that was 12.56
03:36	? Yeah . Okay . And that was in units
03:40	squared . Ok . Something you probably remember . So
03:43	this is not only one , but this is also
03:45	three . He would just worked out . We also
03:47	get this part two here . Okay , part two
03:50	here , which is equal to as you see here
03:54	, it's a I'll just get rid of that for
03:56	a second . We're going to have this distance all
03:58	the way across here . Now , this is not
04:00	only to this is a older diameter , here's the
04:03	entire diamond . So this is gonna be area is
04:05	going to be equal to uh to our which is
04:10	the diameter . Okay , twice the radius . And
04:13	this is going to be times the height here .
04:16	Okay , so these are all our area formulas here
04:19	. So this is going to be equal to to
04:23	our which is two times 2 , which is four
04:27	times the height here , which were given us five
04:30	. Okay , so this is going to be equal
04:32	to 20 . Okay , a nice easy 1 .
04:34	20 units square . So oh um What about I
04:37	write 20 And I'll hit memory plus . So so
04:41	far we should have 32 with these added together .
04:44	32.56 . Okay , I'll get rid of that .
04:47	Okay , so the next one we're going to do
04:49	is part for here and that's this entire semicircular part
04:55	. This semi cylinder part . First off we got
04:57	the higher . Okay , if we were to unravel
05:00	this , if you were to go get a toilet
05:01	cylinder right now and cut it open , cut it
05:04	in half and then and then you can flatten it
05:05	out and you can actually see that we would end
05:07	up with a rectangle . Okay , we're gonna end
05:09	up with a rectangle . That is the same as
05:11	the height here , but also the same as half
05:14	a distance around the circle of half the circumference of
05:16	the circle . So we have to work at the
05:18	circumference of the circle . This distance from here to
05:21	here , we're gonna have to work that out right
05:23	now . I'm going to do this just over here
05:26	. Okay , because this is going to be equal
05:29	to our area here is going to be equal to
05:32	the height times half of the circumference . Do you
05:38	get that ? Okay , so let's work at circumference
05:40	over here , separately . So what is half the
05:43	circumference ? Well , circumference , this is so many
05:47	formulas to remember here equals to hire . Okay ,
05:51	so this is equal to two times pi times the
05:56	radius which we have given us to . All right
05:57	, so it's gonna be the same as four pi
06:00	. Okay . She didn't realize they've used 12.56 .
06:05	12.56 . Okay , because this is actually the same
06:08	sort of calculation we get over here . This is
06:10	our workout area . This is the work of circumference
06:12	just happens to fall that same sort of thing .
06:14	Okay , the same value in this . If we
06:17	have this idea , we're going to end up with
06:20	our circumference being approximately 6.28 . Okay , now let's
06:29	just get a calculator and work it out . So
06:31	the circumference , I'm going to clear that up .
06:32	That circumference is again , we saw that was it's
06:36	too times why times the radius , which is to
06:44	Okay , which is 12.5 , divide that by two
06:48	is where after half the circumference here . Okay .
06:51	And other times it by the higher education is part
06:53	of it's at times the height which is fire .
06:58	Okay , we get 31 .4159 . I'm going to
07:03	also put that in the memory . Okay , so
07:06	this is equal to Uh 6.28 remember Times uh height
07:15	which was five and this is a around about 31.4
07:20	. And so if we total all these together ,
07:22	12.56 and 20 and 31.4 . And I've been putting
07:26	these in the memory as we go along . So
07:28	I don't been hitting memory plus memory plus memory plus
07:31	now I'm gonna hit memory Read , it has all
07:34	those values up for me . So this is the
07:36	same as 12.56 plus 20 which is around about 32.56
07:41	Plus 31.4 . So we should get the answer of
07:45	63.98 . So this is our total equals 63 point
07:54	98 You good with that ? Okay . Hopefully that
07:59	was of some help . Okay . It was a
08:01	bit of a video on the fly . We didn't
08:03	really think too much about it . Typically don't think
08:06	too much about him . I just put them together
08:07	. But anyway , hopefully that was of some help
08:10	. If you have to work these types of things
08:12	out again , emit certain things that you don't need
08:14	to if you don't need this particular rectangle party ,
08:17	it don't put it in . If they're not asking
08:19	for that or that they're making an open cylinder ,
08:21	maybe you don't have to put this particular parts in
08:24	here . So you sort of got these three components
08:27	for components , you got this circle part which is
08:30	a half circles , it's going to end up adding
08:31	as a circle . You've got this part here ,
08:33	which is just going to be twice the I'll get
08:36	rid of this . So we got this circle part
08:37	here , which is this going to be this ,
08:39	you know , this circle part in this circle part
08:41	and it's going to add up to a full circle
08:43	. We've got this rectangular part here which cuts through
08:46	the middle . This is going to be equal to
08:48	twice the radius or diameter times the height . And
08:53	we also have this entire cylinder part . Okay ,
08:56	And this is going to be equal to the half
08:58	of the circumference of this circle , half of it
09:01	times the height here . Okay , that was how
09:04	we work this out over here . Okay . Hopefully
09:07	that was some helpmate . Um we'll catch you later
09:10	. Okay ? See you , bye . Mhm .

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