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The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?

A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches

1 Answer

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The volume of a pyramid that has the same base and height as the prism it is inscribed in is exactly one-third the volume of the prism. This is true for any pyramid that can be inscribed in a prism as long as the base and height are the same1.
Since the volume of the pyramid is 18 cubic inches, then the volume of the prism is 3 times that amount which is 54 cubic inches 2.
Therefore, the answer is D. 54 cubic inches.
User Martijnve
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