Answer:
The ratio of the volumes of the similar solids is 1331:343.
Step-by-step 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 [tex](a/b)^2[/tex], and the ratio of their volumes is [tex](a/b)^3[/tex].
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:
[tex](a/b)^2=(121/49)[/tex]
Taking the square root:
[tex]a/b = \sqrt{121/49}=11/7[/tex]
Thus, the ratio of the volumes is:
[tex](a/b)^3=(11/7)^3=1331/343[/tex]
The ratio of the volumes of the similar solids is 1331:343.
