Question

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

True: The bases are congruent; The volume of the first solid is twice the second; The first has 4xh more surface area.

Reasoning:
- Bases: both are squares with the same side length, so congruent.
- Volumes: V2 = x^2·h, V1 = x^2·(2h) = 2x^2·h, so V1 is twice V2 (ratio 2:1), not 8:1.
- Surface area: SA2 = 2x^2 + 4xh, SA1 = 2x^2 + 4x(2h) = 2x^2 + 8xh, so SA1 − SA2 = 4xh.
- Similarity: false, because corresponding linear dimensions are not all in the same ratio (base sides ratio 1, height ratio 2).