Question

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One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
The bases are congruent.
The solids are similar.
The ratio of the volumes of the first solid to the second solid is 8:1.
The volume of the first solid is twice as much as the volume of the second solid.
If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.

Answer 1

The bases are congruent, the solids are similar, and the ratio of their volumes is 8:1.

Step-by-step explanation:

To determine which statements about the two rectangular solids are true, let's consider the given information. One solid has twice the height of the other solid, but both have the same side length for the base. Here are the true statements:

1. The bases are congruent, as they have the same side length.
2. The solids are similar, since their bases are congruent and their heights are in a ratio of 2:1.
3. The ratio of the volumes of the first solid to the second solid is 8:1, because the ratio of their heights is 2:1 and the ratio of their base areas (which are congruent) is also 2:1. Multiplying the ratios gives us 2*2:1*1, resulting in a ratio of 4:1 for the base areas. Since the height ratio is also 2:1, the overall volume ratio is 4*2:1*1, which simplifies to 8:1.