Answer:
The ratio of the volumes of the similar solids is 1331:343.
Explanation:
Ratios
Given the ratio of two lengths is a:b. Given a two-dimensional shape is similar to another shape, the ratio of their areas is
, and the ratio of their volumes is
.
We know the ratio of the areas of the bases of two similar rectangular prisms is 121:49. Thus, the ratio of its dimensions is:

Taking the square root:

Thus, the ratio of the volumes is:

The ratio of the volumes of the similar solids is 1331:343.