a triangular pyramid and a triangular prism have congruent bases and the same height the triangular pyramid has a volume of 90m3 what is the volume if the prism?

Answers

Answer 1

Answer:

Final answer:

The volume of a prism is calculated by multiplying the base area by the height, since the base and height of the triangular prism are the same as the triangular pyramid whose volume is three times smaller, the volume of the prism is 270 cubic meters.

Explanation:

The volume of a pyramid is calculated by taking one-third the base area times the height (1/3*bh). In the case of the triangular pyramid mentioned, that calculation has given us a volume of 90 cubic meters. A prism, conversely, has a volume equal to the base area times the height (bh). Given both the triangular pyramid and the prism in your question have congruent bases and the same height, the prism's volume would be three times that of the triangular pyramid. Thus, the volume of the prism is 270 cubic meters.

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Answer 2

Answer:

Final answer:

The volume of the triangular prism, with the same congruent bases and height as a triangular pyramid of volume 90 m³, is 270 m³.

Explanation:

The volume of a prism is calculated by multiplying the area of the base by the height. In this case, the triangular pyramid and the triangular prism have congruent (same size) bases and the same heights. Therefore, if we denote the area of the base as A, and the height as h, the volume of the pyramid is calculated as (1/3)Ah, and the volume of the prism is calculated as Ah. From the problem, we know that the volume of the pyramid is 90 m³. We can use this equation to determine the volume of the prism.

Since (1/3)Ah = 90 m³ and we want to find Ah (the volume of the prism), we can multiply both sides of the equation by 3 to solve for Ah:

3 * (1/3)Ah = 3 * 90 m³

Ah = 270 m³

So, the volume of the prism would be 270 m³.

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