Answer:
Yes, the circumference will always double when the radius is doubled
Simple Explanation: For example, 2 is the given radius, we can double 2 and get 4 as our diameter, then times pi. We get 4 pi as our initial circumference.
When we double the radius, we have a given radius of 4, and to find the diameter we get 8. 8 times pi= 8 pi. This is the simple version of the below example
Full Example:
Radius - 3
Pretend the radius is 3, do 3*2 and get the diameter of 6, then times 3.14 equals 18.84. So the current circumference is 18.84.
Now to find the new circumference. Now the radius is 6. To find the diameter we can do 6*2 and get 12. Now to find circumference; 12 x 3.14 = 37.68. 37.68 / 18.84 = 2