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Two rectangular prisms are similar. The ratio of the areas of the bases is 121:49. What is the ratio of the volumes of the similar solids?

User BenDes
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1 Answer

4 votes

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
(a/b)^2, and the ratio of their volumes is
(a/b)^3.

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:


(a/b)^2=(121/49)

Taking the square root:


a/b = √(121/49)=11/7

Thus, the ratio of the volumes is:


(a/b)^3=(11/7)^3=1331/343

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

User TautrimasPajarskas
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8.0k points
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