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Rhea has two cardboard boxes in the shape of rectangular prisms. Each box has the same height and cross-sectional area as the other. Which of the following best describes the relationship between the boxes according to Cavalieri's principle?

AThe boxes are congruent.
BThe surface areas of the boxes are the same.
CThe base of each box has the same perimeter as the other.
DThe volumes of the boxes are the same.

Verified Answer :

Edufirst

Option D. The volume of the boxes are the same.

The formula for the volume of a prism is the area of the base times the height.

Answer:

Option D) The volumes  of the boxes are the same.

Step-by-step explanation:

Given that Rhea has two cardboard boxes in the shape of rectangular prisms. Each box has the same height and cross-sectional area as the other.

Since we are given height and cross sectional area are the same, we see that the bases have same area.   The dimensions need not be congruent.

Hence the boxes need not be congruent

Surface area also need not be congruent since length, width may differ for each prism

The area is the same need not imply perimeter is the same.

Hence only option d) The volumes of the boxes are the same.

is the right answer.

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