Geometry: Circumference of a Circle
This is a free lesson from our course in Geometry
 
   
This lesson defines and explains the basics of a circle, radius, diameter, circumference and their relationship. It will also guide you through determining the circumference of a circle given a radius or diameter or vice-versa. The presentation covering such content will be done by the instructor in own handwriting, using video and with the help of several examples with solution. This will help you understand and master the basics and important formulas and how to use them to solve the problems.
To proceed further you’ll begin to understand about the circle and related different aspects of it. A circle is a shape with all the points at same distance from the center and the distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. The radius of a circle is the distance from the center of a circle to any point on the circle. (More text below video...)
<h2> Geometry - Circumference of a Circle</h2> <p> circle, radius, point, geometry, video, center, circumference, perimeter, distance, line segment, diameter, circumference of a circle, example, solution, math help, practice questions, quizzes</p> <p> A circle is a shape with all points the same distance from the center and the distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. The radius of a circle is the distance from the center of a circle to any point on the circle.</p>
Other useful lessons:
Perimeter of a Polygon
Effect of dimension changes on perimeter
Real World Applications
(Continued from above) A circle has many radii and many diameters, each passing through the center ‘O’. Both the radii and diameter are measured in linear units. E.g. radius of the spoke of a bicycle wheel, and diameter of 8 inch pizza i.e. its diameter is eight inches. The diameter of a circle is twice as long as the radius and this relationship is expressed by (d = 2r), where d is the diameter and r is the radius (Fig: 1).
Relationship between Diameter and Radius
Circumference of a circle
The circumference of a circle is the actual length around the circle which is equal to 360. Circumference is measured in linear units, such as cm, inches etc. The circumference of a circle can be calculated from its radius (r) or diameter (d), using the formula:
C = 2 * r = * 2r or C = * d (the diameter is two times the radius).
pi () is the number needed to compute the circumference of the circle, the numerical value of is 3.141 592 653 589 793... . Generally while computing circumference, value of is taken as 3.14 to simplify the calculations. For example, if the radius of a circle is 3.5 units, then circumference of a circle is 7 units.
Now you’ll explore the other aspects and relationship of a circle (Fig: 2, above):
Center: O- is the exact middle of a circle.
Diameter: AB- must pass through the centre of the circle. The Diameter is equal to twice the radius.
Radius: OC- radius is a line segment that begins from the centre and touches any point on the circle.
Chord: QP- the chord joins any two points on a circle.
Tangent: RS- a line with one point common to the circle.
Arc: QTP- the portion of the circle that is located between two points on the circle.
Sector: OCB- area between two radii and the arc.
Central Angle: COB- formed by two radii, at the center.
Semicircle: APB- can also be called an arc that is exactly half of the circle.
Further you can work out the perimeter of a semicircle i.e. the distance round the outside. Notice that (Fig: 3, below) a semicircle has ‘two edges’. One is half of a circumference and other is the diameter.
Perimeter of a Semicircle
n this case perimeter,
= 1/2 of the circumference of circle + diameter
= (1/2 * * 2.5) + 2.5. Plug in value for , as 3.14
= 6.425 in
Remember:
• the number is the ratio of the circumference of a circle to the diameter.
• value of is approximately 3.14159265358979323846...
• diameter of a circle is twice the radius.
• Given: diameter or radius of a circle, circumference can be found.
• can also find the diameter or radius of the circle using formula given above, if circumference is known.
The video above will explain more in detail about circle, radius, diameter, circumference and their relationship, with the help of several examples.
Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
- All of the Winpossible math tutorials have been designed by top-notch instructors and offer a comprehensive and rigorous math review of that topic.
- We guarantee that any student who studies with Winpossible, will get a firm grasp of the associated problem-solving techniques. Each course has our instructors providing step-by-step solutions to a wide variety of problems, completely demystifying the problem-solving process!
- Winpossible courses have been used by students for help with homework and by homeschoolers.
- Several teachers use Winpossible courses at schools as a supplement for in-class instruction. They also use our course structure to develop course worksheets.
 
       
     
 Copyright © Winpossible, 2010 - 2011
Best viewed in 1024x768 & IE 5.0 or later version