Question

A circle of radius 6 in has a central angle of 2.5 radians. What is the arc length cut off by this angle?

Answer 1

sorry im trying to find the way to word it right.

Answer 2

Thank you for your time.

Answer 3

360 degrees= 2π radians. so 1 radian is 360degrees/2π if you have a full circle you take 360 degrees times the radius, aka 2πr, by converting to the radians first, so it's truly the angle in radians * the radius, but now you have 2.5 radians, Or 143.2394488degrees, so you take (2.5/(2π))(6) and get an arc length of 14.9999in... compared to the full circle of 2π radians, with an arc length of 37.699in

Answer 4

hold on that might not be written well, i have to think it over, it's hard to describe the interaction between radians and degrees

Answer 5

it's more like (2π/2.5)(6) = 14.999
you need to find the ratio between the full circle, and the amount of radians you have

Answer 6

kind of make sense?

Answer 7

Yes, I believe so. Would it be the same if it were cm instead of in?

Answer 8

Same formula, that is.

Answer 9

yes, that just would change the final arc length unit..

Answer 10

correct it stays 2πr for the full circle. and use the same concept of ((2π)/(# of radians you have)*r for arc length.