Volume of a Pyramid | Math with Mr. J - Free Educational videos for Students in K-12

Volume of a Pyramid | Math with Mr. J - By Math with Mr. J

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00:0-1	Welcome to Math with Mr J . In this video
00:05	, I'm going to cover how to find the volume
00:07	of a pyramid . And remember volume is the amount
00:10	of space that a three D . Figure or object
00:13	takes up . Now when it comes to pyramids we
00:17	can use the formula one third times the area of
00:20	the base , times the height . So whatever the
00:23	base is , a rectangle , a square , a
00:26	triangle , etc . Use the correct formula to find
00:30	that area and then plug the area of the base
00:33	into the formula for the volume . Now I do
00:37	want to mention that you can also use the formula
00:40	, the area of the base times the height and
00:44	then divide by three because multiplying by one third is
00:48	the same as dividing by three . Now we'll talk
00:51	about why we multiply by one third or divide by
00:54	three after number one . Knowing why we do this
00:58	will give us a better understanding of the formula .
01:01	So let's jump in the number one where we have
01:04	a pyramid with a square base and then a height
01:08	of four inches . So the first thing that we
01:11	need to do is write out our formula . So
01:14	volume equals one third times the area of the base
01:20	, times the height . Once we have that we
01:23	can plug in . So volume equals one third Times
01:29	the area of the base while we have a square
01:32	. So we can do six times six to calculate
01:36	the area of that base six times six gives us
01:40	36 Times the height of four . Now I do
01:46	want to mention we were able to calculate the area
01:49	of that base using mental math . Don't be afraid
01:52	to come to the side though in order to write
01:55	things out or for a more difficult problem . So
01:58	for example let's go to the bottom left where we
02:02	have some room . We could have gone area equals
02:06	a side length squared . While that's the formula for
02:10	the area of a square and then plug in Side
02:15	length of six squared , which means six times 6
02:19	gives us an area of 36 square inches . So
02:24	again , don't be afraid to come to the side
02:26	if you need to calculate something and then plug that
02:29	area into the formula . So now we're ready to
02:32	solve one third times 36 times four . Now at
02:36	this point you can plug this all into a calculator
02:40	and solve it all in one step . But I
02:42	want to break it down step by step until we
02:45	get to that final volume while one third times 36
02:49	that's going to give us 12 Times 4 to wrap
02:54	things up here . So 12 times four Gives us
02:57	48 and this is cubic inches for our unit of
03:04	measure there . So volume equals 48 cubic inches for
03:10	our final answer . Now I do want to show
03:14	you what the other formula looks like as well for
03:17	number one . So the area of the base times
03:20	the height and then divide by three . So we
03:23	have volume equals the area of the base times the
03:28	height And divide by three . So let's plug in
03:32	volume equals the area of the base was 36 times
03:37	the height of four And divide by three . So
03:41	I'm running out of room there . I'm going to
03:43	go to the side in order to solve this .
03:46	So 36 times four gives us 144 divided by three
03:54	. And that's going to give us a final answer
03:57	of 48 cubic inches . So we got the same
04:02	answer either way , as far as those two formulas
04:06	. So multiplying by one third is the same as
04:10	dividing by three . Both of those are going to
04:13	give us the correct volume . Now I do want
04:15	to talk about why we multiply by one third or
04:19	divide by three to help us better understand this formula
04:23	. So if we take our pyramid , put it
04:25	in a prism with the same base and height ,
04:29	let me try to draw that so we can visualize
04:32	what I mean . So a prism with the same
04:35	base in same height . Now this won't be the
04:40	best drawing but I think it will get the point
04:43	across here . So think of it like putting it
04:47	in a box with the same exact height and base
04:54	. So we put the pyramid in a prism again
04:57	with the same base and height . That pyramid is
05:01	going to be exactly one third , the volume of
05:05	that prism . Now we find the volume of a
05:08	prism by using the formula , the area of the
05:11	base times the height . So the exact same thing
05:15	as the pyramid formula , but without the one third
05:19	or divide by three . And again we multiply by
05:22	one third or divide by three because a pyramid is
05:26	exactly one third , the volume of a prism with
05:30	the same base and height . So let's move on
05:33	to number two . Where we have a pyramid with
05:36	a rectangular base and the height of 11 m .
05:40	And the first thing that we need to do right
05:42	out the formula . So volume equals one third times
05:49	the area of the base , times the height .
05:52	Now we plug in so one third Times the area
05:57	of the base while we have a rectangle . So
05:59	we can do length times with so eight times seven
06:05	. That gives us 56 times the height of 11
06:11	m . So now we're ready to solve one third
06:15	times 56 times 11 . Now I'm going to do
06:20	56 times 11 1st for number two . Unlike number
06:24	one , where we had something compatible with that .
06:26	One third , we had one third times 36 got
06:30	a nice clean hole number of 12 . In the
06:33	case of number two , we don't have anything compatible
06:36	with that . One third . So again , 56
06:39	times 11 is what I'm going to do first here
06:42	and that's going to give us one third times 600
06:48	16 . Now 1 3rd time 616 is going to
06:53	give us an answer of 205 And I'm going to
06:58	round this decimal to the nearest 100th , 33/100 and
07:03	this is cubic meters . So our final answer 205
07:09	and 33/100 cubic meters . So there you have it
07:14	there is how you find the volume of a pyramid
07:17	, one third times the area of the base ,
07:20	times the height , Or the area of the base
07:24	times the height and then divide by three . I
07:28	hope that helped . Thanks so much for watching until
07:31	next time . Peace . Yeah . Yeah . Yeah
00:0-1	.

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