Two bottles are similar solids. The surface area of the smaller bottle is 12 cm2 and the larger bottle is 108 cm2. What is the ratio of their volumes?

6. Similar Bottles

Step 1: Understand the relationship between surface areas and volumes of similar solids.
For two similar solids, the ratio of their surface areas is equal to the square of the ratio of their corresponding linear dimensions (scale factor, $k$), and the ratio of their volumes is equal to the cube of the ratio of their corresponding linear dimensions.
Let $A_1$ and $V_1$ be the surface area and volume of the smaller bottle, and $A_2$ and $V_2$ be for the larger bottle.
Given: $A_1 = 12 \text{ cm}^2$, $A_2 = 108 \text{ cm}^2$.

Step