If s denotes the length of the arc of a circle of radius r subtendes by a central angle 0, find the missing quantity

Question

r=17.31 centimeters, 0= 6.2 radians, s=?

Answer 1

The angle is given in radians so we convert that to degrees.

π radians = 180 degrees so (6.2 radians)(180 degrees)/(π radians) = 355.234 degrees.

The circumference of the circle of radius 17.31 cm = 2 π r = (2)(π)(17.31 cm) = 108.31 cm

We want to find the length of s at 355.234 degrees so we find the ratio to a full circle of 360 degrees and multiply our circumference by that to get the length of the arc s.

[(355.234)/(360)](108.31) = (0.9868)(108.31) = 107.32 cm.

So the length of our arc s is 107.32 cm.

Answer 2

s = r*0

s = 17.31 * 6.2 = 107.322