ARC Length Worksheet
ARC Length Worksheet
In geometrical mathematics, various types of shapes and figures are defined in the
Euclidean geometrical plane.
A circle can be easily described as a simple geometrical figure which is formed by the
collection of several points around the central of the circle.
The shape of circle in geometry plays an important role in the real world situation.
According to mathematical definition, circle can be specified as a closed surface
which is figured by various circumference points around the central point of the circle.
In mathematics various types of properties that are related to the circle, are defined.
Arc is one of them.
An `arc' in geometrical circle, can be defined as a closed frame of a differential
segment of a differential curve on the 2 - D planes. In simple language we can define
arc as a circular arc, which is considered as a part of circumference of the circle.
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In traditional way, the letter`s' is used to initialize the length of an arc, which is
commonly known as arc length.
In mathematics, the arc length can be defined as a part of circle. In short we can say
that arc length can be calculated when circumference of circle is known because the
ratio of the circumference to the diameter is the basis of the radian measure.
In general arc length worksheet of a circle can be described with the `r' and `'. In the
given arc length worksheet the symbol `r' is used for denoting the radius of circle and
the symbol `' is used for denoting the angle of a circle, which is used for measuring
an angle in radian with the circle center.
Arc length worksheet describe that the central angle of the circle equals to the `',
because
l / c = / 2 * pi,
Above `l' shows the arc length of a circle and `c' is used for denoting the
circumference of the circle. Now by using substitution we can represent the above
notation as:
l / 2* pi * r = / 2 * pi (Note: as we know that circumference of circle = 2 * pi * r
)
Now we can perform the solving process of arc length `L', in terms of `' that yields:
l = ,
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In mathematics, the measure of arc length can be calculated either in the form of unit
length or they can also be calculated in the form of degree.
The arc length is the portion of the circle, which can be determined by the size of its
corresponding central angle. In measure of arc length, the concept of proportion is
used that evaluates the part of the circle to the whole circle either in form of degree or
in unit measure.
Angle / 360 = l / c,
Example: Suppose in any question given that the measure of the angle is 90o and the
circumference is 24 inches then we need to calculate be the measure of an arc
length?
Solution: when we proceed to solve the problem then we use the above given
formula, which are shown in the following process:
Angle / 360 = l / c
90 / 360 = l / 24,
360 * l = 2160,
l = 2160 / 360,
l = 6.


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