In any circle the following ratios are equal
We know that angle subtended by whole circumference is .
If r is the radius then Length of whole circumference is
radian has length
dividing both side by we have
1 radian has r length
1 radian = r length equation a
=> since we have to find value of circumference for we
multiply both side of equation a with .
therefore, length of required arc is
we have to find how much is this as fraction of total circumference of circle
fraction of circumference = value of arc length / total length of circumference
fraction of circumference =
Thus, the given arc is 1/3 of circumference of circle.
The central angle of the arc is .
The circumference of an arc of a circle is given as:
where C= circumference of the circle
θ = central angle of the arc
Therefore, the circumference of the arc is:
The circumference of the arc will be 3/10 of the circumference of the circle.
Length of an arc
If the central angle of the arc is
Length of an arc
Ratio of the length of the arc to the circumference
Therefore, the arc is of the circumference is this arc.
Arc Length is 1/4th of the circumference .
Here we need to find fraction of the circumference is this arc when An arc subtends a central angle measuring radians ! Let's find out :
We know that circumference of an arc subtending a central angle of x is :
Therefore , Arc Length is 1/4th of the circumference .
The arc is one-third of the circumference.
The area of a circumference = 2πr
C = 2πr ... (1)
If an arc subtends a central angle measuring 2π/3 rad,
The length of the arc = rθ
Given θ = 2π/3
Length of the arc L = r(2π)/3
L = 2πr/3... (2)
L = 1/3(2πr)
Since C = 2πr
L = 1/3C
This shows that the arc is one-third of the circumference.