Final answer:
The diameter of the purple circle is 24 cm because the diameter of a circle is always twice the radius (2r), and in this case, the given radius is 12 cm.
Step-by-step explanation:
To find the diameter of the purple circle when the given radius is 12 cm, simply use the basic geometric formula that states the diameter of a circle is twice the length of the radius. This is expressed mathematically as D = 2r. Therefore, for a circle with a radius (r) of 12 cm, the diameter (D) is calculated as:
D = 2 × 12 cm = 24 cm.
Thus, the diameter of the purple circle is 24 cm.