The Diameter, Radius, and Circumference of Circles
Circles have been around since as long as the earth has been around. People were able to see natural circles by observing the moon, the sun, and other various naturally circular shapes.
The first technological invention using a circular shape, however, wasn’t until 3500 B.C, and it was the invention of the potter’s wheel. Then, 300 years later, they were used for the wheels of chariots. As people began to see the value, and use for circular shaped objects, they begin to study circles.
Things like radius, diameter, and circumference are terms that helps us to keep track of various measurements of a circle.
So, now, let’s take a look what each of these measurements represent.
First, let’s define midpoint so you’ll understand what I’m talking about as I reference it. The midpoint is the exact center of the circle. That’s it.
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 one edge all the way to the other side, and running through the midpoint of the circle. The diameter of a circle is represented by the lowercase letter “d.”
Circumference- is the distance around the outside edge of a 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 a circle, as if it were a string, and lay it out to measure. This length would be equivalent to the circumference. However, since a circle has a continuous curve, we use the word circumference rather than perimeter to distinguish it.
Now that we’ve looked at what the radius, diameter, and circumference are, let’s look at how to calculate each one.
If someone were to just hand you a piece of paper with a circle on it…. Well that would be pretty weird.. Actually.
But let’s say we wanted to find the radius, diameter, and circumference of the circle; and all we have is a ruler.
The easiest thing to start with, would be to take the ruler and measure, from the center, the length between each outer edge. The diameter.
Let’s say, that when we measured, we got a length of 9cm for the diameter. Well, 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 two.
So, when we take 9 and divide it by 2 we get a radius length of 4.5cm.
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 will need to use a formula.
The formula for the circumference of a circle is C=pi x d, or it can be written as C=2 x pi x r.
You may be asking, ‘well where did pi come from, and why do we all the sudden get the circumference if we multiply said pi by our diameter? Who decided that?” If you are not asking that question… You should, and I’m going to answer it anyways.
Pi is a symbol we use in mathematics to represent the number 3.14. And actually that is just pi rounded to the nearest hundredth. 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 this 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 got the formula for the circumference of a circle.
Now, let’s use the circle with the diameter of 9cm, and radius of 4.5 cm, that we’ve been using, and calculate the circumference.
I’m going to use the formula with the diameter.
So, C= pi x d. We just need to plug in our numbers. C= (3.14)(9cm)= 28.26cm.
And there we have it. To practice, try drawing a circle on a piece of paper, and measure your diameter with a rule. Then, find your radius, and circumference.
I hope this video was helpful. For further help subscribe to our channel right here.
See you next time!