Volume of Rectangular Prisms - Free Educational videos for Students in K-12

Volume of Rectangular Prisms - By Anywhere Math

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00:0-1	Welcome to anywhere , Math . I'm Jeff Jacobson and
00:01	today we're gonna learn how to find the volume of
00:04	rectangular prisms . Let's get started . Before we get
00:26	to this example , let's talk about what exactly volume
00:29	is the volume of a solid measures the amount of
00:32	space it occupies . Another word for that is its
00:35	capacity . Okay . That's what volume is . Okay
00:40	. Instead of surface area where you're going around the
00:42	outside , right ? The face is the area of
00:44	all the faces . Now we're talking about the inside
00:47	how much space it occupies . You see volume all
00:51	the time . When you go to the grocery store
00:53	and you buy a coke , you see maybe it's
00:55	a liter bottle of coke . That's how much ,
00:59	that's the capacity . That's how much coke is in
01:01	that bottle . That's volume . Or you buy a
01:03	gallon of milk , right ? A gallon , that's
01:06	the volume of milk in that bottle . Um ,
01:09	when you have things that are small , it can
01:11	be very easy to measure volume . Right ? If
01:13	you're if you're cooking using something like a measuring cup
01:17	, right , with your recipe , well , you're
01:19	measuring volume how much milk you might need for to
01:22	make some cookies or something . And if it's liquid
01:24	, it's it's quite easy to measure volume . But
01:27	when we have something that's solid , where we couldn't
01:29	just pour in here and figure out how much is
01:31	in there , it's more difficult . Or if you
01:34	have something like a swimming pool , it would take
01:37	a really long time to just do this with all
01:40	the water and figure out the volume of that swimming
01:42	pool . So instead we have formulas that we can
01:46	use to find the volume of things like that .
01:49	So we're not going to use this today . Uh
01:52	let's get to our first example and figure out how
01:54	you can use math to find volume . Okay ,
01:57	example , one find the volume of the prism .
02:00	Now , first , this is a rectangular prism and
02:04	with a rectangular prism or a square prism , there's
02:07	two formulas that we can use uh to find the
02:10	volume of this first one you may be familiar with
02:13	and that's just volume equals length , times width ,
02:17	times height . Okay , so length here times the
02:22	width , how deep it goes back times the height
02:26	. Right ? That will give you the volume .
02:28	Uh your units are always going to be cubic units
02:31	. Remember , because this is three dimensional and we're
02:33	doing meters times meters , times meters . So at
02:36	the very end , I just gotta remember , I'm
02:38	gonna have meters cubed . Ok . Um but if
02:42	we think about this , this first part length times
02:45	with , well that's going to give us the area
02:49	of our base , which is right here . So
02:56	the other and there were times in it by the
02:59	height , basically . How how much you can think
03:01	of it when you find that area of that base
03:05	times it by the height . So it's like you're
03:07	raising that up , you're stretching that out and filling
03:10	that space . Um and that will give you that
03:12	volume . So the other forms that I'm going to
03:15	show you is volume equals area of the base ,
03:20	which we use a capital B to represent that times
03:24	the height . Okay , that's another formula . And
03:27	the nice thing about this , so area of the
03:33	base . Okay . Area of the base . Yeah
03:38	, these both would work for this because basically when
03:41	you do length times width , that is the area
03:43	of the base , right ? And then your times
03:44	into by height . The nice thing about this is
03:48	that I'm going to put a star next to this
03:51	, is that it will work for any prisms .
03:54	If you have a triangular prism you find the area
03:57	of the base , that area of that triangle ,
04:00	times it by the height . If you have a
04:02	pentagonal prism , find the area that pentagon and then
04:06	multiply it by the height , even cylinders . When
04:09	you get two cylinders , you find the area of
04:11	that circle , that base circle times it by the
04:14	height and that will give you the volume . So
04:16	that's a really useful um really useful formula because it
04:21	can work for so many different types of solids .
04:24	Whereas this only is going to work for rectangular or
04:28	a square prism . Okay , um so just make
04:32	sure you you know both of those . Uh we're
04:35	only going to be dealing with rectangular prisms in this
04:38	lesson . So it's not a big deal to to
04:42	worry about that . Anyway , let's solve for volume
04:45	. So let's go ahead blank times with Time's tight
04:49	. So volume is going to be 78 times one
04:54	half times the height . Just five , eight .
05:02	Any time a multiplying fractions , I'm always hoping and
05:04	trying to simplify first . Unfortunately , here there is
05:08	nothing that I can simplify . Uh , so I'm
05:12	just multiplying straight across . Seven times one is seven
05:14	times five is 35 . Uh , I'm sorry .
05:20	That's supposed to be 1/2 My fault . one half
05:25	. Okay , I'm gonna do eight times 8 at
05:27	64 times two is 128 . And then if you
05:31	remember the thing , you gotta remember units at the
05:34	very end meters , transmitters , transmitters will give me
05:37	meters cube and you show that with a little three
05:42	up there . Okay . Instead of squared . Right
05:46	? So if I'll answer 35 over 128 m cubed
05:51	. Here's something to try on your own . Here's
06:00	our last example . Find the height . So they
06:04	give us a rectangular prism . They tell us the
06:07	volume already The volume is 1,792" cube or cubic inches
06:14	. But they want us to find the height .
06:16	We don't know the height . So what we're gonna
06:18	do is we're gonna set up an equation and uh
06:21	solve for h solve for height . So we know
06:25	that the formula is lifetime's worth times height will give
06:29	us the volume right ? Volume equals length , times
06:33	width , times height . Now let's substitute in the
06:36	things , we know what we know the volume .
06:38	So that's 1,792 . We know the length 7" .
06:45	We know the width 16" . We don't know the
06:50	height , that's our unknown . Uh So here's our
06:55	equation we're gonna solve for H . First thing I'm
06:57	gonna do is I'm gonna simplify it a little .
06:59	So 1792 7 times 16 . Well that's 71 12
07:08	, whoops ! 100 12 Times 812 H . Mhm
07:15	. Hopefully you remember a little bit of algebra .
07:18	So I've been one step equation . Uh This is
07:20	100 and 12 times H . So to undo that
07:23	multiplication I need to divide both sides by 112 .
07:29	Keep that equation balance . Uh That becomes one and
07:33	goes away so I get H . Is equal to
07:37	well let's see . Um I'll go ahead . I've
07:40	got room over here . I'm not really sure .
07:43	So let's do some Division 792 . 1 12 .
07:50	Can you see that ? Yes . 112 into that
07:53	goes once . 1 12 to track . I get
07:56	76 Bring down the two 112 into that . Let's
08:03	try six times six times that is 12 , carry
08:07	the 1676 . Perfect . Okay , so H is
08:14	16 . Now I got to remember my units .
08:17	These were all inches so final answer . The height
08:22	is equal to 16 inches . Yeah , 9" cubes
08:28	. Remember that was for the volume . This is
08:30	just height . So 16" . Here's some more to
08:34	try on your own . Thank you so much for
08:42	watching and if you like this video , please subscribe
08:51	. Yeah .

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