Finding the radius of a circle

Question

What is the radius of a circle in which an angle of 3 radians cuts off an arc length of 30cm?

Answer 1

We can use the formula s = rθ, where s is the arc length, r is the radius, and θ is the radian measure of the angle.

 

Substituting into the formula, we have 30 = 3r.  So, r = 10 cm.

 

 

Answer 2

radian measure of a central angle=arc length/length of radius

3=30/r

r=30/3

r=10 cm

or,...

arc length=(arc measure/180)*(pi)(r)

30=(3 radians/180)(pi)(r) where 3 radians=3*180/(pi) degrees

30=(3*[180/pi]/180)(pi)(r)

simplify: 3*[180/pi]*(1/180)=3/pi, 3/pi*(pi)(r)=3r

30=3r

r=10 cm again