The two solids are similar, and the ratio between the lengths of their edges is 3:8. What is the ratio of their surface areas?A.27:512B.3:8C.6:16D.9:64

1. Break Down the Problem

To determine the ratio of the surface areas of two similar solids, we need to understand the relationship between the ratio of their corresponding dimensions (in this case, edges) and their surface areas.

2. Relevant Concepts

For similar solids, if the ratio of the lengths of their edges is given as $a:b$, then the ratio of their surface areas is given by $a^2:b^2$.

3. Analysis and Detail

Given the ratio of the lengths of their edges is $3:8$.

1. Let $a = 3$ and $b = 8$.
2. The ratio of surface areas will be calculated as: $\left(\frac{a}{b}\right)^2 = \left(\frac{3}{8}\right)^2 = \frac{3^2}{8^2} = \frac{9}{64}$

4. Verify and Summarize

The calculations confirm that the ratio of the surface areas is indeed $9:64$.

Final Answer

The ratio of the surface areas of the two solids is $\text{9:64}$. Therefore, the correct option is D. 9:64.