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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)