Explanation:

- When comparing cubes, note that their surface areas are proportional to the square of their side lengths.

- If the ratio of the total surface areas is 49 : 81, then the ratio of the side lengths is the square root of 49 : 81, which is 7 : 9.

- Volumes of cubes are proportional to the cube of their side lengths.

- Therefore, the ratio of their volumes is 7³ : 9³.

- Calculating these, 7³ = 343 and 9³ = 729.

- So, the correct ratio for their volumes is 343 : 729.

Option:1 - 343 : 729