Final answer:
The area of the base of the volcano model is 26.7 square centimeters.
Step-by-step explanation:
To find the area of the base of the volcano model, we need to first determine its volume. Given that the model's volume is 586.7 cubic centimeters and its height is 22 cm, we can divide the volume by the height to find the area of the base. So, the area of the base of the model is 26.7 centimeters squared.