hey it's Kalei in this lesson we will learn how to find the circumference in
the area of circles let's go before we jump into our calculations for circles
we need to know the parts of a circle the first one is the center point which
is equidistant from every part of the outline or the edge of the circle there
are two important measures of a circle the first is the diameter it is the
measure of the distance across the center of the circle like this we can
also measure the distance from the center of the circle to the outer edge
like this this one is called the radius of the circle do you notice any
relationships between the diameter and the radius that's right the radius is
half of the diameter let's do a quick example if I have a circle with a
diameter of 4 what is the radius of my circle yeah I have to divide by 2 and I
get a radius of 2 now if I have a circle with a radius of 3 what is the diameter
of my circle yeah I have to multiply by 2 and we get a diameter of 6 we call the
perimeter of a circle the circumference the circumference is the distance around
the circle since there are no sides on a circle we can't use our formula for
perimeter where we add the lengths of all the sides instead we have to find a
relationship between the diameter of the circle and the perimeter of the circle
luckily for us the ancient Greeks spent a lot of time thinking about circles and
ratios an ancient Greek named Archimedes
especially loved to think about the ratio between the circumference and the
diameter of different circles let's explore what he discovered here I have a
circle with the diameter of 1 and it's been painted along the edge or along the
circumference with blue paint now I'm gonna roll my circle along this number
line here and see where the blue paint ends and that will tell me what my
circumference is and once I know my circumference I want to know the
relationship between the diameter of my circle and the circumference of my
circle all right so I know my diameter is 1 I'm going to unroll my circle
that's the length of our diameter 1 so we're going past that we're getting all
the way to 3 and we have a little bit more so this distance right here where
my blue paint ends that's the circumference of my circle and it is a
distance of 3.14 so this tells me that the relationship between my diameter and
my circumference is 1/2 3.14 now that we know the relationship or the ratio
between diameter and circumference we can come up with our formula for
circumference we discovered that the diameter times approximately 3.14 equals
the circumference but there are something special about the number 3.14
we call it PI and we use this symbol to represent it pi is actually an
irrational number that means it is a never-ending decimal the numbers just
keep going on forever but we can shorten it to 3.14 and this gives us a very
accurate calculation for circumference sometimes calculators have a PI button
that uses more decimal places and calculations this is good for very
precise measurements but for us we just use 3.14 so we can write our
formula as see the circumference is equal to D the diameter times pi I can
also plug in the radius because we know D is equal to 2r we can also say C is
equal to 2 times pi times R now let's do this example of finding the
circumference of a circle so I have this distance is given to me and since it
goes from the edge to the center of the circle I know that this is equal to my
radius R so I can plug it into our formula here circumference is equal to 2
times pi times my radius which is 5 feet so now if I multiply my 2 and my 5
together I get 10 feet and I'm multiplying all of that by PI and 10
feet times remember PI we can say it's equal to 3 point 1 4 here and now if I
multiply 10 feet by 3.14 I get 31.4 feet and that's the circumference or the
distance all the way around my circle nice work now to find the area of a
circle we need to know pi and the radius of the circle and we can use the formula
area equals PI R squared remember that squaring a number means multiplying that
number by itself so let's do this example for finding the area together so
I have this distance given to me here which goes to the center of my circle so
I know that this is equal to my radius R so I can play that into my formula here
area is equal to PI and then my radius which is 4 inches squared and so now
this is telling me I have 4 inches times 4 inches that's what my squared means so
if I multiply my fours together I get 16 and if I multiply my inches together I
get inches squared so now I have a is equal to PI times 16
inches squared and if I multiply 3.14 my approximation for pi by 16 inches
squared I get you might not know that off the top of your head and that's okay
I get 50 point to 4 inches squared remember our units for area are always
to the power of two now let's do this one here if I have this measurement that
goes all the way across I know that twelve inches is equal to my diameter
but in my formula here I have an R but remember R is equal to half of the
diameter so if I have 12 inches for my diameter my radius will be half of that
six inches good it's now you can plug that into my formula a is equal to PI
six inches squared so now if I'm squaring this I square my number and I
square my units I get PI 36 inches squared now I'm going to multiply PI my
approximation 3.14 times 36 inches squared and if you don't know that off
the top of your head that's all right total comes to 113 point oh four inches
squared so that would be the total area of this circle good job now you know the
parts of a circle and the formulas for circumference and area practice what
you've learned by doing the online games and quizzes have fun and remember to
always be clever