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### Course: Algebra basics > Unit 1

Lesson 10: Circumference and area of circles# Radius, diameter, & circumference

Learn the relationship between the radius, diameter, and circumference of a circle.

## What is a circle?

We've all seen circles before. They have this perfectly round shape, which makes them perfect for hoola-hooping!

Every circle has a center, which is a point that lies exactly at the... well... center of the circle.
A circle is a shape where distance from the center to the edge of the circle is always the same:

You might have suspected this before, but in fact, the distance from the center of a circle to any point on the circle itself is exactly the same.

## Radius of a circle

This distance is called the radius of the circle.

## Diameter of a circle

The diameter is the length of the line through the center that touches two points on the edge of the circle.

Notice that a diameter is really just made up of two radii (by the way, "radii" is just the plural form of radius):

So, the diameter $d$ of a circle is twice the radius $r$ :

## Circumference of a circle

The circumference is the distance around a circle (its perimeter!):

Here are two circles with their circumference and diameter labeled:

Let's look at the ratio of the circumference to diameter of each circle:

Circle 1 | Circle 2 | |
---|---|---|

Fascinating! The ratio of the circumference $C$ to diameter $d$ of both circles is ${3.14159\text{\u2026}}$

This turns out to be true for all circles, which makes the number ${3.14159\text{\u2026}}$ one of the most important numbers in all of math! We call the number pi (pronounced like the dessert!) and give it its own symbol ${\pi}$ .

Multiplying both sides of the formula by $d$ gives us

which lets us find the circumference $C$ of any circle as long as we know the diameter $d$ .

## Using the formula $C=\pi d$

Let's find the circumference of the following circle:

The diameter is $10$ , so we can plug $d=10$ into the formula $C=\pi d$ :

That's it! We can just leave our answer like that in terms of $\pi $ . So, the circumference of the circle is $10\pi $ units.

Your turn to give it a try!

## Challenge problem

## Want to join the conversation?

- How do we find the circumference when the radius is given? (<im a lil confuse)(140 votes)
- if the
**diameter**is given we find the circumference by diameter x pi, so if the radius is half the value of the diameter then if you are only given the**radius**we find the circumference by radius x 2 x pi because radius x 2 = diameter(154 votes)

- what happens if the circle is not perfectly round?(21 votes)
- Then technically it's not a circle(93 votes)

- why is this so hard :((42 votes)
- can you tell me the drivation of this formula(19 votes)
- Here the Greek letter π represents a constant, approximately equal to 3.14159, which is equal to the ratio of the circumference of any circle to its diameter. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons.(57 votes)

- i have a question why do you need to know this(23 votes)
- If you are asking why you need to know math, let me explain:

How are you going to get a job?

{Let me give you an example: My brother joined the Army a few months ago, but before he joined he had to take the ASVAB a test mostly on math skills which determines the job you will get-do you want to be a toilet-cleaner or a soldier?-}

You may not join the Army but in life you have to face what you may not like.

Math may not be your favorite, but just do your best!

YOU CAN DO IT!

Have a BLESSED day!

M.L.M.(29 votes)

- how do i find the circumference if the diameter is given(2 votes)
- Hi, to find the circumference and you have the diameter all you have to do is do the diameter times pi and the answer you get is the circumference. Another formula to find the circumference is if you have the diameter you divide the diameter by 2 and you get the radius. Once you have the radius you times the radius by 2 and times it by pie and then you get the circumference. Here are the two different formulas for finding the circumference:

C = πd

C = 2πr

d = diameter, C = circumference, and r = radius

Hope this helped :)(40 votes)

- What is zero divided by zero(12 votes)
- Interesting question! Think of 0 divided by 0 as the answer to the question “what number times 0 is 0?”. Because any number times 0 is 0, 0 divided by 0 can be anything! For this reason, 0 divided by 0 is called indeterminate.

If you take calculus later on, you will frequently encounter the indeterminate expression 0 divided by 0 in limit problems. What this means is that the result is inconclusive, so more work is required to calculate the limit or determine that the limit doesn’t exist.(19 votes)

- Do you guys like to answer in terms of pi or do you guys like to get the answer in a decimal?(10 votes)
- If you are using that value for another calculation, it's better to leave it in exact form (like you said, in terms of pi). Otherwise, probably show the answer as a decimal to a certain amount after putting it in the calculator.

You don't want to round an answer that's used for further calculations as you lose some well-needed precision.(12 votes)

- How to I find the diameter of a circle when the circumference is given?(7 votes)
- Just divide the circumference by pi or 3.14.(6 votes)