The Solution:
The correct answer is 8:27 or 8 to 27.
Given that the lateral areas of two similar prisms have the ratio below:

We are required to find the ratio of their volumes in the same format and order as the above-given ratio.
Step 1:
We shall find the ratio of their side lengths.
![\begin{gathered} \sqrt[]{32}\colon\text{ }\sqrt[]{72} \\ \sqrt[]{16*2}\colon\text{ }\sqrt[]{36*2} \\ 4\text{ }\sqrt[]{2}\colon6\text{ }\sqrt[]{2} \\ 2\colon3 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/74ascog7e87qhdxlv5w5hnob78ekt10pj2.png)
Step 2:
We shall find the ratio of their volumes.

Thus, the ratio of their volumes is 8 to 27.
Therefore, the correct answer is 8:27 or (8 to 27)