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## Praxis Core Math

### Unit 1: Lesson 5

Geometry- Properties of shapes | Lesson
- Properties of shapes | Worked example
- Angles | Lesson
- Angles | Worked example
- Congruence and similarity | Lesson
- Congruence and similarity | Worked example
- Circles | Lesson
- Circles | Worked example
- Perimeter, area, and volume | Lesson
- Perimeter, area, and volume | Worked example

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# Circles | Lesson

## What are circles?

Circles are round. They don't have any corners. All of the points on a circle are the same distance from the

**center**.That distance is called the

**radius**, and it's usually represented by start color #1fab54, r, end color #1fab54. The**diameter**, represented by start color #aa87ff, d, end color #aa87ff, is twice as long as the radius.Because circles are so symmetrical, simply knowing either the radius or the diameter can tell us a lot about a circle.

### What skills are tested?

- Calculating the circumference of a circle
- Calculating the radius or diameter of a circle when given the circumference
- Calculating the area of a circle
- Calculating the radius or diameter of a circle when given the area

## What's a circumference?

The

**circumference**of a circle is the distance around it. It's usually represented by start color #11accd, C, end color #11accd. We can calculate start color #11accd, C, end color #11accd using either start color #aa87ff, d, end color #aa87ff or start color #1fab54, r, end color #1fab54, but to do so we need to know about the number pi.Various ancient civilizations found that the ratio of circumference to diameter, or start fraction, start color #11accd, C, end color #11accd, divided by, start color #aa87ff, d, end color #aa87ff, end fraction, is the same for circles of all sizes. This ratio, pi, is a little greater than 3. For our purposes, the approximation pi, approximately equals, 3, point, 14 works.

The formula for start color #11accd, C, end color #11accd, the circumference of the circle with diameter start color #aa87ff, d, end color #aa87ff, is:

The formula for start color #11accd, C, end color #11accd, the circumference of the circle with radius start color #1fab54, r, end color #1fab54, is:

With each formula, we can also calculate start color #aa87ff, d, end color #aa87ff or start color #1fab54, r, end color #1fab54 when start color #11accd, C, end color #11accd is given. To do so, we:

- Write down the appropriate equation.
- Plug in the value for start color #11accd, C, end color #11accd.
- Solve for start color #aa87ff, d, end color #aa87ff or start color #1fab54, r, end color #1fab54.

## What's a circle's area?

The

**area**of a circle is the amount of flat space inside the circle's circumference.The formula for start color #ca337c, A, end color #ca337c, the area of a circle with radius start color #1fab54, r, end color #1fab54, is:

We can also calculate start color #1fab54, r, end color #1fab54 when start color #ca337c, A, end color #ca337c is given. To do so, we:

- Write down the area equation.
- Plug in the value for start color #ca337c, A, end color #ca337c.
- Solve for start color #1fab54, r, end color #1fab54.
- For the diameter start color #aa87ff, d, end color #aa87ff, multiply start color #1fab54, r, end color #1fab54 by 2.

## Your turn!

## Things to remember

The diameter (d) is twice as long as the radius (r), and 3, point, 14 is a common approximation for pi.

The circumference (C) formulas are:

The area (A) formula is:

## Want to join the conversation?

- How do you find the area and perimeter of segments of a circle? (ex. 1/4 of a circle)(3 votes)
- yes of course there is a formula for each:

(note: write them down so they are easier to read )

area of a sector:`(θ/360) × π × r^2`

area of a segment:`A = (½) × r^2 × [((π × θ)/180) – sin(θ)]`

perimeter of a sector:`r × (((θ × π)/180) +2)`

to find the perimeter of a segment you will need to add the (LENGTH OF ARC + LENGTH OF CHORD):`((θ × 2πr)/360) + (2r × sin(θ/2))`

hope this helps you <3(4 votes)

- i have no clue what i am doing why is this so hard ... :((2 votes)
- It isn't hard once you practice....try watching math antics on it..it's what helped me!(1 vote)