Given:
Central angle of a sector = 72 degrees
Intercepted arc length = 44 cm
To find:
The radius of the circle.
Solution:
We know that, the arc length is
[tex]s=2pi r\dfrac{\theta }{360^\circ}[/tex]
Where, r is the radius of the circle, [tex]\theta[/tex] is the central angle in degrees.
Putting [tex]s=44,\pi=3.14[/tex] and [tex]\theta = 72^\circ[/tex], we get
[tex]44=2(3.14)r\dfrac{72^\circ }{360^\circ}[/tex]
[tex]44=6.28r(0.2)[/tex]
[tex]44=1.256r[/tex]
Divide both sides by 1.256.
[tex]\dfrac{44}{1.256}=r[/tex]
[tex]35.031847=r[/tex]
[tex]r=35.03[/tex]
Therefore, the radius of the circle is about 35.03 cm.
