Answer :
Answer:
The diameter of the circle is 10 cm.
Step-by-step explanation:
As
- A central angle of a circle measures 1.2 radians, and
- The length of the related intercepted arc measures 6 cm.
The arc length formula is given by:
[tex]s\:=\:r\theta[/tex]
where
- [tex]r[/tex] is the radius of the circle
- [tex]\theta[/tex] is the central angle in radians
First lets find r,
[tex]\:\frac{s}{\theta \:}\:=\:r[/tex]
[tex]\frac{6}{1.2\:}\:=\:r[/tex] ∵ s = 6 cm and [tex]\theta[/tex] = 1.2 radians
[tex]\:r\:=\:5\:cm[/tex]
As
- Diameter 'd' is 2r.
so
[tex]d\:=\:2r[/tex]
[tex]d\:=\:2\left(5\right)[/tex]
[tex]d = 10[/tex] cm
Therefore, the diameter of the circle is 10 cm.