The ratio of the lengths of corresponding parts in two similar solids is 4:1. What is the ratio of their surface areas?A.16:1B.4:1C.8:1D.64:1

Break Down the Problem

1. Identify the ratio of the lengths of corresponding parts in the two similar solids, which is given as 4:1.
2. Determine how the ratio of lengths relates to the ratio of surface areas for similar solids.

Relevant Concepts

3. The surface area ratio of two similar solids is the square of the ratio of their corresponding linear dimensions. If the ratio of lengths is $r$, then the ratio of surface areas $S$ is given by: $S = r^2$

Analysis and Detail

4. Given the length ratio $r = \frac{4}{1}$, we can compute the ratio of the surface areas: $S = \left(\frac{4}{1}\right)^2 = \frac{16}{1}$

Verify and Summarize

5. The calculations confirm that the surface area ratio of the two solids is $16:1$.

Final Answer

The ratio of their surface areas is A. 16:1.