Question

A rectangular pyramid and rectangular prism have congruent bases and heights. The area of each of the bases is 36 in.2.

Which statement is true, where h represents the height of the figure?
o The volume of the pyramid is V = 36h in.3 and the volume of the prism is V = 36h in.
o The volume of the pyramid is V = 12h in.3 and the volume of the prism is V = 36h in.3.
o The volume of the pyramid is V = 36h in.3 and the volume of the prism is V = 12h in.3.
o The volume of the pyramid is V = 12h in.) and the volume of the prism is V = 12h in.3.

Answer 1

The volume of the rectangular prism is V = 36h in.³ and the volume of the rectangular pyramid is V = 12h in.³, based on their congruent base areas and heights.

Step-by-step explanation:

We are tasked with comparing the volume of a rectangular pyramid and a rectangular prism with congruent bases and equal heights. The volume of a prism is calculated by multiplying the area of the base by the height (V = Ah), and therefore, for the rectangular prism with a base area of 36 in.² and height h, the volume is V = 36h in.³.

For a pyramid, the volume formula is one third the base area multiplied by the height (V = (1/3)Ah). Given the same base area and height, the volume of the rectangular pyramid would be V = (1/3) * 36h in.³. This simplifies to V = 12h in.³.

Therefore, it is true that the volume of the pyramid is V = 12h in.³ and the volume of the prism is V = 36h in.³.