Question

A rectangular pyramid and a 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?

A) The volume of the pyramid is V=36h in.³, and the volume of the prism is V=36h in.³.
B) The volume of the pyramid is V=12h in.³, and the volume of the prism is V=36h in.³.
C) The volume of the pyramid is V=36h in.³, and the volume of the prism is V=12h in.³.
D) The volume of the pyramid is V=12h in.³, and the volume of the prism is V=12h in.³.

Answer 1

The statement that is true is A) The volume of the pyramid is V=36h in.³, and the volume of the prism is V=36h in.³.

Step-by-step explanation:

To find the volume of a rectangular pyramid, we use the formula V = (1/3) × base area × height.

Since the pyramid and prism have congruent bases and heights, the volume of both figures will be proportional to the base area and height.Since the base area is 36 in.² for both the pyramid and prism, the volume for each figure will be V = (1/3) × 36 × h = 12h in.³. Therefore, the statement A) The volume of the pyramid is V=36h in.³, and the volume of the prism is V=36h in.³. is correct.