trigonometry problem

Question

Consider an angle, and a circle centered at the angle's vertex. The circle's radius is 3 cm long and the angle subtends an arc that is 5.4 cm long.

A. A circle is centered at the angle's vertex, and the circle's radius is 6 cm long. The subtended arc is how long in cm? 

Answer 1

3 cm times the angle, measured in radians = 5.4 cm

the angle = 5.4/3 = 1.8 radians

6 cm x 1.8 radians = 10.8 cm

= arc length when the radius =6 cm

5.4x2 = 10.8

double the radius and the arc length doubles

the circumference of a circle with radius =3 is 6pi

circumference of a circle with radius =6 is 12 pi

the circumference double when radius doubles and

so does any arc length regardless of the angle's size