Geometry - Help with Circumference, Diameter and Radius

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     In order for a circle to be perfectly round, all the points around the edge must be exactly the same distance away from the center.  If you were to draw a straight line through the center of the circle, the line would measure 180 degrees.  Since both sides of the line are part of the circle, the circle would measure 360 degrees.
 
     Any line from the center of the circle to any point on the edge of the circle is called the radius.  Any line from one side of the circle to the other, through the center is called the diameter.  The diameter is the same length as 2 radii (the plural of radius).  The perimeter of a circle is called the circumference.  The measurement around the outside rim of a circle is the circumference.  To find the area of a circle, we use the formulae Area =πr².  The symbol π (pronounced 'pie') is found by dividing the circumference measure by the diameter measure.  When we do this, we get 3.146.  Therefore, pie is the ratio of the circumference to the diameter.  The ratio of diameter to circumference is equal for all circles therefore all circles are similar. 

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     If you want to calculate the circumference and you only know the diameter, you multiply the diameter times pie and you get the circumference.  And, if you have the circumference and you want to find the diameter, divide by pie.
 
So,   

Circumference = Diameter x π

Diameter = Circumference

             π

Here are some other concepts that students must become familiar with when studying circle geometry:

A chord is a line segment from any edge of the circle to any other edge.

A semicircle is exactly one half of a circle.

An arc is a section of the circumference of a circle.

A minor arc is an arc less than 180 degrees.

A sector is the area covered from an arc to the center of a circle that is bounded by two radii.

A tangent is a line outside the circle that meets the circle at only one point.
 
By becoming familiar with circle concepts, students will gain a better understanding of circle geometry. 

Tutorgiant.com provides Circle geometry lessons with worksheets.

See some of the lessons in our video library.

AREA - Lesson (D) Area of a Circle (Grades 7-8)

CIRCLES - Circle Geometry (Grade 8)

CIRCLES - Lesson (A) Radius and Diameter (Grades 7-8)
CIRCLES - Lesson (B) Finding Circumference (Grades 7-8)
CIRCLES - Lesson (C) Using Circumference to find Radius and Diameter (Grades 7-8)
CIRCLES - Lesson (D) Arcs and Central Angles (also considered Geometry) (Grades 9-10)
CIRCLES - Lesson (D) Chords and Inscribed Angles (also a geometry lesson) (Grades 9-10)
VOLUME - Lesson (D) Volume of Cylinders (Grades 7-8)

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by Stuart Ackerman        

     MSc.Ed.,B.A.