Main content

## 7th grade

### Course: 7th grade > Unit 6

Lesson 1: Area and circumference of circles- Geometry FAQ
- Radius, diameter, circumference & π
- Labeling parts of a circle
- Radius, diameter, & circumference
- Radius and diameter
- Radius & diameter from circumference
- Relating circumference and area
- Circumference of a circle
- Area of a circle
- Area of a circle
- Partial circle area and arc length
- Circumference of parts of circles
- Area of parts of circles
- Circumference review
- Area of circles review

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# Radius, diameter, & circumference

CCSS.Math:

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 | |
---|---|---|

start fraction, start text, C, i, r, c, u, m, f, e, r, e, n, c, e, end text, divided by, start text, D, i, a, m, e, t, e, r, end text, end fraction: | start fraction, 3, point, 14159, point, point, point, divided by, 1, end fraction, equals, start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39 | start fraction, 6, point, 28318, point, point, point, divided by, 2, end fraction, equals, start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39 |

Fascinating! The ratio of the circumference C to diameter d of both circles is start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39

This turns out to be true for all circles, which makes the number start color #e84d39, 3, point, 14159, point, point, point, end color #e84d39 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 start color #e84d39, pi, end color #e84d39.

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, equals, pi, d

Let's find the circumference of the following circle:

The diameter is 10, so we can plug d, equals, 10 into the formula C, equals, 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)(90 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(89 votes)

- can you tell me the drivation of this formula(16 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.(33 votes)

- what happens if the circle is not perfectly round?(9 votes)
- Then technically it's not a circle(37 votes)

- chicken sandwich(16 votes)
- im in your walls(13 votes)

- why is this so hard :((11 votes)
- it's not. you just have to understand(12 votes)

- What is zero divided by zero(8 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.(10 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 :)(20 votes)

- When can I find the diameter of the circumference of a circle of a circle? How can I find the diameter of a circle?(6 votes)
- oh! For example your radius is 5 cm. Remember the diameter is two times the radius. So 5x2=10 so your diameter is 10. bye(6 votes)

- How to I find the diameter of a circle when the circumference is given?(6 votes)
- Just divide the circumference by pi or 3.14.(4 votes)

- someone give me pizza(5 votes)
- ok just look at my profile(1 vote)