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This video is provided as supplementary material
for courses taught at Howard Community College and
in this video I'm going to explain how to find the volume of cylinders
and prisms.
So I've drawn a couple prisms here. The first one is a triangular prism.
It's got a triangle as both of the bases.
Those triangles are parallel to each other and they're congruent with each other.
Then I've got a rectangular prism. The bases of
a rectangular prism are rectangles which are congruent with each other
and parallel to each other. And I've got a cylinder.
So for a cylinder both the bases are going to be circles
that are parallel to each other and also congruent with each other.
Now to find the volume for each of these different figures
we can you a separate formula for each one, but I'm going to use a general form that will
work for
any prism and also for any cylinder. That formula is going to be
that the volume equals the area of the base
times the height. So let's apply that formula to a couple of different figures.
I'll start out with a triangular prism.
I've drawn triangular prism here.
Its height is 5 inches and I've also drawn a separate picture of its
base,
so we can see that for the triangle that forms the base
it's got one side which is 4 inches long
and it's got an altitude that's 3 inches high.
So the formula we're going to use is that the volume of this prism
will equal the area of the base
times the height. We know what the height is,
but we have to find the area of the base.
The base is a triangle. We know the formula for the
area of a triangle. It's the base
times the height divided by 2.
So the base is 4 and
the height is 3. So we'll multiply 4 times 3, divide that by 2...
4 times 3 is 12, and 12 divided by 2 is 6.
So the area of the base is 6 inches.
The height is 5 inches. So that means the volume
is going to be 6 inches, the area of the base,
times the height, which is 5 inches,
or 30 cubic inches.
When you're dealing with volume, make sure that your
unit measurements are cubic.
So all we did was apply the formula -- volume is the area the base
times the height. We found what the area of the base was
and we multiplied that by the height.
Let's see how this works for a cylinder. So I've got a cylinder here.
The height of the cylinder is 7 inches and
the circle that forms
each of the bases has a diameter 4 inches.
So we're going to have to find the area
of the base. That means we need the area of the circle.
So the formula for the area of a circle
is pi
times the radius squared. We're not given the radius, we're given the diameter.
Remember the radius is one half the diameter.
So that means we're going to have pi
times 2-squared.
2-squared is 4, so the
area of each of the bases is going to be 4 pi.
Now we'll take our
formula for the volume of a cylinder or prism
it's going to be the volume is the area of the base times the height.
The base has an area of 4 pi
and the height is 7, so we're going to end up with
28 pi. Once again,
that's cubic inches. And if we wanted to, of course
we could take that pi and either use a rough estimate for it, something like 3.14,
or we could put this in a calculator multiply it by 28,
and we'd find out approximately how many cubic inches
we have in the cylinder.
So to recap the whole thing -- for any cylinder
or any prism, it doesn't matter if it's a triangular prism
or a rectangular prism or whether the bases are
pentagons or 7-sided figures or octagons,
for any prism or any cylinder
the formula you can use to find the volume is going to be
the area of the base times the height of the prism
or the cylinder.
Take care, I'll see you next time.