Given:
Length of arc AB is 4 units.
The measure of central angle corresponding to arc AB is 30 degrees.
To find:
The circumference of the circle.
Solution:
The formula for arc length is:
[tex]s=2\pi r\dfrac{\theta }{360^\circ}[/tex]
Where, r is the radius and [tex]\theta[/tex] is the central angle.
It is also written as:
[tex]s=C\dfrac{\theta }{360^\circ}[/tex]
Where, C is the circumference of the circle.
Putting [tex]s=4,\theta =30^\circ[/tex] in the above formula, we get
[tex]4=C\dfrac{30^\circ}{360^\circ}[/tex]
[tex]4=\dfrac{1}{12}C[/tex]
Multiply both sides by 12.
[tex]4\times 12=C[/tex]
[tex]48=C[/tex]
The circumference of the circle is 48 units.
Therefore, the correct option is A.
