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 viceversa. 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...)
(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).
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.
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.
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