How long is the arc subtended by an angle of 4p/3 radians on a circle of radius 15cm?

Question

How long is the arc subtended by an angle of 4π/3 radians on a circle of radius 15cm?

Answer 1

arc length s = r * theta, where theta is in radians.

 

So here, s = 15cm * 4pi/3 = 20pi cm.

 

4pi/3 * (180 degrees/pi radians) = 240 degrees which is 2/3 of 360 degrees, and therefore 2/3 of the circumference.

 

The circumference is 2(pi)*r or 2(pi) (15cm) = 30 pi cm, so our answer ought to be 2/3 of that, which is 20 pi cm. This checks.