Answer: Circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is a constant.
We know that the diameter is twice the radius (d = 2r).
So when we increase the circumference of the circle from 12π cm to 18π cm, we are increasing the radius from r to r'.
To find the increase in diameter, we can use the formula for the diameter, and subtract the original diameter from the new diameter.
d' = 2r' and d = 2r
d' - d = 2r' - 2r
We know that the relationship between circumference and radius is C = 2πr.
So we can write:
12π = 2πr and 18π = 2πr'
r = 6/π and r' = 9/π
then
d' - d = 2r' - 2r = 2(9/π) - 2(6/π) = 18/π - 12/π = 6/π
Therefore, the diameter must increase by 6/π cm in order to increase the circumference of the circle from 12π cm to 18π cm.
Explanation: