7
AssignmentMultiple Select

Volume of Cylinders, Cones, and Spheres

Question 7 • (OC27) GEO-1206310-S2-Degele-VOL7006P

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
A
The bases are congruent.
B
The solids are similar.
C
The ratio of the volumes of the first solid to the second solid is 8:1.
D
The volume of the first solid is twice as much as the volume of the second solid.
E
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.

Explanation

Both solids have square bases with the same side length, so their bases are congruent (A). Their volumes are x²h and x²(2h), so the first volume is twice the second, not eight times as large (D). Their surface areas are 2x² + 4xh and 2x² + 8xh, respectively, so the first has 4xh more surface area (E). They are not similar because the base side lengths stay the same while the heights differ.

AI-written and checked against the verified answer.

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