Relationships in Volume Between Triangular Prisms and Pyramids

T.i.P.S.

Students should connect their prior knowledge of relating the volume of rectangular prisms and pyramids to triangular prisms and pyramids. The relationship between a triangular prism and a triangular pyramid with equal bases and heights is that the volume of the prism is three times the volume of the pyramid. Students should physically model this relationship using manipulatives such as water, rice or beans.

Example

Explain the relationship between the volume of a triangular prism and a triangular pyramid with congruent bases and heights in the given model and connect that relationship to the formulas for volume of a triangular prism and triangular pyramid.

Hint

Possible Solutions

TEKS

8.8 Expressions, equations, and relationships. The student applies mathematical process standards to develop geometric relationships with volume. The student is expected to:

(B) explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights and connect that relationship to the formulas

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