Hey guys! Welcome to this video on the radius diameter and circumference of a circle.
Circles have been around as long as the earth has been around.
People were able to see natural circles by observing the moon, the Sun, and other various natural circular shapes.
The first technological invention using a circular shape, however, wasn't until 3500 BC
and it was the invention of the potters wheel.
Then three hundred years later they were used for wheels of chariots.
As people began to see the value and the use for circular shaped objects they begin to study circles.
Things like radius diameter and circumference are terms that
help us to keep track of various measurements of a circle
So now let's take a look at what each of these measurements represent.
First let's define midpoint so you'll understand what I'm talking about as I reference it.
So that's our circle.
The midpoint is the exact center of the circle. So,
somewhere in here.
Now let's look at these other terms.
Radius is the length from the midpoint of the circle to the outer edge of the circle.
The radius is represented by the lowercase letter r
Diameter is the full length of the circle running from the edge through the midpoint all the way to the other side.
That is this whole length right here. The diameter of a circle is represented by the letter D
Now circumference is the distance around the outside edge of this circle.
Circumference is represented by the uppercase letter C.
Circumference is comparable to the perimeter of a shape like a parallelogram.
If you were to cut the line of this circle out and then lay it out as if it were a string,
the length of that would be equivalent to its circumference.
However, since the circle has a continuous curve,
we use the word circumference rather than perimeter to distinguish it.
Now that we've looked at what a radius diameter and circumference are
let's look at how to calculate each one.
If some of them are just kind of hand you a piece of paper with a circle on it
Well actually they're pretty weird
but let's say we wanted to find the radius diameter and circumference of that circle and all we
have is a ruler the easiest thing to start with would be to take the ruler
and measure from the very center of the circle the length between the outer edge
that would be the diameter.
Let's say that when we measure we got a length of 9 centimeters for the diameter
While we know that if our radius runs from the midpoint
to the outer edge then all we have to do to find the length of
our radius would be to divide the length of the diameter by 2.
So take 9 divided by 2 we get a radius length of
the formula for the radius can be written as
r=d/2 and the formula for diameter can be written as d=2r
Now to find the circumference of a circle we need to use a formula.
The formula for the circumference of a circle is
C=pi*d
or it can be written as
C=2*pi*r
either one worse now you may be asking
well where did pi come from and why do we all said and get the circumference if
we multiply said PI by our diameter.
Who decided that.
If you're not asking that question you should
and I'm gonna answer it anyways.
Pi is a symbol we use mathematics to represent the number 3.14
and actually that is just pi rounded to the nearest hundredths.
Pi actually has no end and no predictable pattern it just keeps going.
However when you see the symbol pi generally and in our case
3.14 will suffice.
Pi is not a random number that mathematicians made up
and declared we will multiply the diameter by the number every time and call it a circumference
On the contrary,
pi was discovered to be the constant ratio between the circumference and the diameter.
That is why and how we get the formula for the circumference of a circle
Now let's take the circle with the diameter of 9 centimeters in radius
of 4.5 centimeters and calculate the circumference.
I'm going to use the formula with the diameter for this one.
So circumference equals I'm going to just rewrite the formula
help us follow our work equals pi times diameter.
So now all we need to do is we need to plug in our number for diameter.
This is equal to and we also we said Pi was equal to 3.14
times nine centimeters
and here's our answer.
Now to practice try drawing a circle on a piece of paper
and measure your diameter with a ruler.
Then find your radius and circumference
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