the circumference of a circle is 64 cm.find the diameter ,the radius,the length of an arc of 190

Accepted Solution

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 diameterwe know that the circumference of a circle is equal to[tex]C=\pi D[/tex]whereD is the diameterwe 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 radiuswe know thatThe radius is half the diameterso[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 degreeswe know thatThe circumference of the circle subtends a central angle of 360 degreessousing proportion[tex]\frac{64}{360}=\frac{x}{190}\\ \\ x=64*190/360\\ \\x=33.78\ cm[/tex]