Question

based on cavalieris principle, will the two prisms have the same volume?
yes, the heights of both prisms are the same and they have the same cross - sectional area. therefore, they will have the same volume.
no, they will not be same. although the heights are the same, the cross - sections are different shapes.

Explanation:

Step1: Calculate cross - sectional area of first prism

The cross - sectional area of the first prism (rectangle) is \(A_1 = 6\times2=12\)

Step2: Calculate cross - sectional area of second prism

The cross - sectional area of the second prism (parallelogram) is \(A_2 = 6\times4 = 24\)

Since \(A_1
eq A_2\), according to Cavalieri's Principle (which states that if two solids have the same height and the same cross - sectional area at every level, then they have the same volume), the two prisms do not meet the condition of having the same cross - sectional area.

Answer:

No, they will not be same. Although the heights are the same, the cross - sections are different shapes.