Welcome to a lesson on the circumference of a circle. The distance around a
circle has a special name called the circumference.
So you can think of the circumference of a circle as the perimeter of a circle. To
find the circumference of a circle
we use one of the two formulas, the two formulas are equivalent.
First, we have the formula C equals two times pi, times r, where c is the
circumference and r is the radius. And because two times the radius is equal to
the diameter,
we can also give the circumference formula as C equals pi times d. In the
formula the symbol is pronounced pi and is defined as the circumference of any
circle divided by its diameter. So pi is equal to the circumference divided by
the diameter for any size circle. For example, if we consider this circle here.
If we determine the circumference, which is the distance around the circle
and divide it by the diameter,
this will give us the value of pi. We often replace pi with the approximate
value of three point one, four, or twenty-two sevenths.
Let's look at two examples.
We're asked to find the circumference of each of the following circles, leave the
answer first in exact form, meaning leave the pie in the circumference. And then
in rounded form, to the hundredths place value, which means two decimal places.
So looking at the first circle,
notice how we're given the radius r is equal to four inches and therefore, we will
use the circumference formula C equals two times pi, times r. And now we substitute
four inches for r. Sometimes we'll leave the units off until we determine this
product.
But I'm going to go ahead and include the units this time. So we'll say
the circumference C is equal to two times pi, times four inches.
And because two times four is equal to eight, the exact circumference is eight pi inches.
And now we'll use a calculator and get a decimal approximation for the
circumference to the hundredths place value. Many calculators have a pi button,
so if we use the pi button instead of the approximate value of three point one, four for pi,
it will affect our rounded results. Let's go ahead and show both. Using the pi button
we would have eight and then pi is second in the exponent key, enter, to the hundredths
place value
this is approximately twenty-five point one, three inches.
Using the pi button is more accurate than using three point one, four,
so let's do a comparison. If we enter eight times three point one, four,
notice how we get the approximate value of twenty-five point one, two, which is slightly different
than what we get when we use the pi key,
because the pi key uses a better approximation for pi. Now for our second
example, notice how we're given the diameter and therefore, this time we'll
use the formula C equals pi times d. So we substitute twelve point four, four for the diameter. So
we have C equals pi times twelve point four, four meters. And therefore, the exact circumference is
twelve point four, four pi meters. And now we'll go back to the calculator to get a decimal approximation
for the circumference. And again, we will compare the values using the pi
button, which is using three point one, four. Using the pi button we'd have twelve point four, four times pi,
enter, which would be approximately thirty-nine point zero eight meters. And if we enter twelve point four, four
times three point one, four,
notice how we get approximately thirty-nine point zero, six. I'm going to use a more accurate
approximation of thirty-nine point zero, eight.
But if your directions do say use three point one, four for pi make
sure that's what you enter on your calculator.
I hope you found this helpful.