In this video, we will be going over the
volume of a cylinder, We will be reviewing the area formula. We will
explain derived units. We will define a cylinder. We will explain pi. We will
show three units for volume in the metric system and three units for volume
in the United States system. Here, we have the formula for the area of
a circle and this is our first derived unit. A derived unit is what you have
when you take two or more units and put them together to make a measurement.
The radius represents the length. Since the radius is squared, we have length times length when we multiply those together we get a unit
squared So now, we are going to take our circle
and we are going to stretch it out and make a cylinder. A cylinder is a solid
object with identical flat ends that are circular or elliptical and has one
curved side. Now this area formula works great for the circle on the very end, but
we have to move into volume because we are adding an extra length right here
to make a cylinder. So the volume formula is pretty much the area formula with an
extra length. So, the area has two units or units squared and the volume formula
has three lengths or units cubed or units to the third power. Now, let’s take a quick second to explain
pi. Pi is an irrational number. It is also known as a mathematical constant.
A mathematical constant is a number that arises naturally. Now, being an irrational,
number, in decimal form irrational numbers never end and they never repeat.
So, pi never ends and it never repeats. So, I am going to show you two forms of pi that are an approximation. Here we have the two approximations. The top will be
in a decimal. The bottom will be in a fraction. And as we show the decimal
equivalent of both of them, the first three digits are the ones that are good.
Now, let’s try some examples. We have our formula here. We are going to plug in our
height, which is 14. Next we are going to plug in our radius, which is three. And
that is three squared, so three squared equals nine.
Now, we have pi, so we are going to multiply all that together. 3.14 times
nine times 14 gives us 395 point 64. And, since we are dealing with volume, it is going to be units cubed. So now, let’s try this with some fractions. We are going to
have our height, which is four over five. And we are going to plug that into our
formula. Next, our radius is going to be one over five. And when we plug that into
our formula for the radius, we have to square it. So that is going to be 1 over
25. Now, pi, The fraction form of pi is 22 over 7. So, we plug all that into our
formula. So we have 22 over 7, times 1 over 25, times 4 over 5. And that gives us
88 over 875. And, since we are doing volume, that is going to be units cubed. Now, if we were in the metric system, the units could be millimeters cubed,
centimeters cubed, or meters cubed. Over in the United States standard system, they could be inches cubed, feet cubed as well as yards cubed. That is it, Take care