Hey guys! Welcome to this video on the radius, diameter, and circumference of a circle.
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Circles have been around for 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 BC, 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.
Midpoint of a Circle
First, let&#;s define midpoint, so you&#;ll understand what I&#;m talking about as I reference it. Here&#;s a circle:
The midpoint is the exact center of the circle, where the dot is.
Radius vs. Diameter
Radius of a Circle
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 of a Circle
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 \(d\).
Circumference of a Circle
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 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.
Calculations
If someone were to just kinda hand you a piece of paper with a circle on it&#;. Well, actually, that would be 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.
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Let&#;s say, that when we measured, we got a length of 9 cm 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 2.
So, when we take 9 and divide it by 2 we get a radius length of 4.5 cm.
Radius Formula
The formula for the radius can be written as \(r=\frac{d}{2}\)
Diameter Formula
The formula for diameter can be written as \(d=2r\)
Circumference Formula
The formula for the circumference of a circle is \(C=\pi \times d\), or it can be written as \(C=2\times \pi \times r\). Either one works!
Now, 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 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 got the formula for the circumference of a circle.
Now, let&#;s take the circle with the diameter of 9 cm, and radius of 4.5 cm, and calculate the circumference.
I&#;m going to use the formula with the diameter for this one.
So, circumference equals (I&#;m just gonna rewrite the formula to help us follow our work), \(C=\pi \times d\), equals pi times diameter. So now all we need to do is to plug in our number for diameter.
\(C=(3.14)(9\text{ cm})=28.26\text{ cm}\)
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.
I hope that this video has been helpful for you.
See you guys next time!
This article was co-authored by Joseph Quinones . Joseph Quinones is a High School Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. This article has been viewed 4,145,082 times.
Article Summary
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The diameter of a circle is the distance straight across the circle from one side to the other at its center. Depending on what other information you have about the circle, there are a few different ways to calculate the diameter. If you know the radius of the circle, all you have to do is multiply it by 2 to get the diameter. For instance, a circle with a radius of 2 cm would have a diameter of 4 cm. You can also find the diameter of a circle if you know its circumference, or the distance all the way around the outside of the circle. Just divide the circumference by π to find the diameter. For example, if your circle has a circumference of 23 inches, the diameter would be 23/π, or approximately 7.32 inches. If you only know the area of the circle, use the formula diameter = 2 x &#;(area/π). So, if the area of the circle is 25 square centimeters, the diameter would be 2 x &#;(25/π), or approximately 5.64 centimeters. You can also measure the diameter of a drawing of a circle, but you&#;ll need to find the exact center of the circle to make an accurate measurement. The easiest way to do this is to draw two parallel chords across the circle. A chord is a straight line that connects any two points on the outer edge of the circle. Once you&#;ve drawn your chords, draw a diagonal line starting at the point where one chord intersects the edge of the circle, then connect it to the opposite point on the chord below. Draw a second line crossing the first one, connecting the other two points of the chords. The point where the two lines intersect will be the exact center of the circle. Draw a line through that point from one side of the circle to the other, and measure the length of that line to get the diameter. Read the article to learn how to calculate the diameter of a circle using a ruler!
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