Question

Find the indicated arc length.

The arc corresponding to a central angle of π/3 in a circle of radius 6 inches

Answer 1

The circumference of this circle is

C = 2*π*r

C = 2*π*6

C = 12π


The angle π/3 is (π/3)/(2π) = 1/6 of the way to completing a full circle, so you multiply the circumference with 1/6 to get

12π*(1/6) = 12π/6 = 2π


So the arc is 2π units long

Answer 2

thanks so much :) i really appreciate it!! so 6.28 degrees is the length of the arc?

Answer 3

no 6.28 units (not degrees or radians)

Answer 4

oh in this case, the units are inches

so 6.28 inches roughly

Answer 5

oh ok i see, thanks so much

Answer 6

so 6.28 is the answer? or is there more steps afterwards

Answer 7

degrees and radians apply to angles and not lengths

Answer 8

no that's pretty much it, 6.28 is a rough approximation

Answer 9

thank you so much for the explanation i really appreciate it!! :)

Answer 10

you're welcome