Answer:
Part 1) The diameter is [tex]D=20.38\ cm[/tex]
Part 2) The radius is [tex]r=10.19\ cm[/tex]
Part 3) The length of an arc is equal to [tex]33.78\ cm[/tex]
Step-by-step explanation:
Part 1) Find the diameter
we know that the circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]C=64\ cm[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for D
[tex]64=(3.14)D[/tex]
[tex]D=64/(3.14)=20.38\ cm[/tex]
Part 2) Find the radius
we know that
The radius is half the diameter
so
[tex]r=D/2[/tex]
substitute
[tex]r=20.38/2=10.19\ cm[/tex]
Part 3) Find the length of an arc of 190 degrees
we know that
The circumference of the circle subtends a central angle of 360 degrees
so
using proportion
[tex]\frac{64}{360}=\frac{x}{190}\\ \\ x=64*190/360\\ \\x=33.78\ cm[/tex]
