Audio Transcript Auto-generated
- 00:01 - 00:05
the aura and welcome to this video, we're calculating the
- 00:05 - 00:06
volume of prisons.
- 00:08 - 00:11
The formula to find us depends on the object itself,
- 00:13 - 00:15
but there will always be a common feature that the
- 00:15 - 00:21
units will always be units cubed, the first group of
- 00:21 - 00:23
those with a constant cross section.
- 00:24 - 00:25
And we'll just have a quick look at what we
- 00:25 - 00:26
mean by that.
- 00:26 - 00:31
So if we have something like a um a rod
- 00:31 - 00:35
or a cylinder got curved, if we look at the
- 00:35 - 00:38
end of it, it means that anywhere we cut the
- 00:38 - 00:46
shape and look at the end, that end and that
- 00:46 - 00:49
end and that end and that end will all be
- 00:49 - 00:50
exactly the same.
- 00:53 - 00:57
So the objects in this group include Q.
- 00:57 - 01:00
Boyd's cylinders and prisons.
- 01:01 - 01:03
So they are the ones with the constant cross section.
- 01:07 - 01:09
And although they have their own formula for working it
- 01:09 - 01:13
out, there's a common way of calculating the volume and
- 01:13 - 01:16
that is you take the cross section of that object
- 01:17 - 01:19
and you multiply it by the link.
- 01:21 - 01:24
So as a formula, we have this, the volume of
- 01:24 - 01:27
the prism is equal to the area of the cross
- 01:27 - 01:30
section times by the link.
- 01:31 - 01:33
Let's have a look at it for a couple of
- 01:34 - 01:37
what? For three basic prism type shapes that we talked
- 01:37 - 01:41
about. So the volume is equal for a Q.
- 01:41 - 01:44
Boyd, it's the height times the width or that's the
- 01:44 - 01:47
base surface, Base area times the length.
- 01:48 - 01:52
Triangular prism is the area of the end, which is
- 01:52 - 01:55
half the base times the height times the links.
- 01:56 - 01:59
And the cylinder is the area of the end, which
- 01:59 - 02:01
will be a circle, times are link.
- 02:02 - 02:03
So they're all similar.
- 02:03 - 02:06
So let's just look at what they look like in
- 02:07 - 02:10
um as examples of these objects.
- 02:13 - 02:16
So here we have our three basic shapes that our
- 02:16 - 02:19
prisons. So the first one, we're going to look at
- 02:19 - 02:20
the rectangular or the Q.
- 02:21 - 02:24
Boyd one and the surface area of the end of
- 02:24 - 02:26
that. Let's look at dimensions.
- 02:26 - 02:29
It's two x 4 x three.
- 02:30 - 02:31
And we'll call these all meters.
- 02:33 - 02:37
So the the area of the end In this case
- 02:38 - 02:42
is two times 4 In the volume.
- 02:42 - 02:43
So it's eight.
- 02:44 - 02:44
The volume.
- 02:45 - 02:50
He calls this super the area times the length, times
- 02:50 - 02:54
33 24 meters cubed.
- 02:54 - 02:58
Ok, so we're talking about this being the cross section
- 02:59 - 03:00
or the end.
- 03:01 - 03:02
So this is this part here.
- 03:03 - 03:04
Two times four is 8.
- 03:04 - 03:07
And then we're times in it by the length here.
- 03:08 - 03:10
This will be the cross section and this one will
- 03:10 - 03:11
be here too.
- 03:11 - 03:13
So let's just look at those now.
- 03:14 - 03:15
Um we're going to call the diameter.
- 03:16 - 03:21
So the radius Is equal to five on this one.
- 03:23 - 03:27
So the area of the end as a member for
- 03:27 - 03:27
a circle.
- 03:28 - 03:34
It's um pi r squared times five squared and that's
- 03:34 - 03:38
going to give us um Let's just leave it like
- 03:38 - 03:45
that for now and the volume as High times five
- 03:45 - 03:47
squared times the length.
- 03:47 - 03:48
And the length was 21.
- 03:50 - 03:52
Okay, times 21.
- 03:53 - 03:54
And that's going to give us.
- 03:55 - 04:08
Um So this gives us 1, 649 points 336 Members
- 04:09 - 04:09
did earlier.
- 04:09 - 04:12
Anytime you've got pie, you're going to have to round
- 04:12 - 04:12
your answer.
- 04:13 - 04:15
So I'm going to round it to 49.
- 04:17 - 04:19
We're going to ignore those because they weren't involved here.
- 04:20 - 04:21
We'll call them meters again.
- 04:22 - 04:27
So some meters cubed And it's surrounded 20 DP.
- 04:28 - 04:31
Okay. And the last one will look at is our
- 04:31 - 04:37
triangle. And we know that the Based as 11 cm.
- 04:38 - 04:42
This is 16 sent tomatoes and the height.
- 04:44 - 04:45
Um So how we're going to show the height, Let's
- 04:45 - 04:49
just show the height here Is going to be four
- 04:50 - 04:54
cm. So the area of the end.
- 04:55 - 05:00
So wrong colour area of the end or the cross
- 05:00 - 05:09
section? It calls half base height Equals half of 11
- 05:10 - 05:17
times um four half the best times the height and
- 05:17 - 05:22
the volume is going to equal a half Times 11
- 05:23 - 05:26
times for times the length, which was 16.
- 05:28 - 05:32
And that's going to give us an answer of three
- 05:34 - 05:37
52 centimetres cubed.
- 05:38 - 05:43
Okay, so that was just a quick look at using
- 05:43 - 05:46
these three formulas here, looking at how the consistent thing
- 05:47 - 05:50
where she worked out the surface area of the end
- 05:50 - 05:52
or the cross section if we want to call it
- 05:52 - 05:55
that and what it looks like when you're finished.
- 05:56 - 05:58
So now you can go back to the scheme of
- 05:58 - 06:01
works, Look at what questions and what pages you're supposed
- 06:01 - 06:02
to be working on.
- 06:03 - 06:05
And good luck, I hope it goes well.