IM Geo.5.13 Lesson: Building a Volume Formula for a Pyramid

Two solids are shown. For each solid, draw and label a prism or cylinder that has a base congruent to the solid’s and a height equal to the solid’s.
Here is a triangular prism.
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[/img][br][br][size=150]Suppose we split the prism into pyramids like the ones you built earlier. The first pyramid is split off by slicing through points [math]E[/math], [math]D[/math], and [math]C[/math]. The remaining part of the prism is sliced through [math]B[/math], [math]C[/math], and [math]D[/math].[/size][br][br][table][tr][td]P1[/td][td]P2[/td][td]P3[/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][br][br][size=150]Using the pyramids you built, compare pyramids P1 and P3.[/size][br][br][size=100]Think of the faces marked P1 and P3 as the bases of the pyramids. These triangles are the two bases of the original prism. [br]How do the areas of these two bases compare?[/size]
[size=100]How do the heights of pyramids P1 and P3 compare? Explain your reasoning.[/size][br]
[size=100]How do the volumes of pyramids P1 and P3 compare? Explain your reasoning.[/size][br]
[size=150]Using the pyramids you built, compare pyramids P2 and P3.[/size][br][br][size=100]Think of the gray shaded triangles as the bases of the pyramids. These are formed by slicing one of the prism’s rectangular faces down its diagonal. [br]How do the areas of these two bases compare?[/size][br]
[size=100]The heights of pyramids P2 and P3 are equal because when assembled into the prism, the height lines coincide along the length of the prism. How, then, do the volumes of these pyramids compare? Explain your reasoning.[br][/size]
[size=150]Based on your answers, how does the volume of each pyramid compare to the volume of the prism?[/size][br]
[size=150]How could you use this information to find the volume of one of the pyramids?[/size][br]
[size=150]Each solid in the image has height 6 units. The area of each solid’s base is 10 square units. A cross section has been created in each by dilating the base using the apex as a center with scale factor [math]k=0.5[/math].[/size][br][br][img]data:image/png;base64,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[/img][br][br]Calculate the area of each of the 3 cross sections.
[size=150][size=100]Suppose a new cross section was created in each solid, all at the same height, using some scale factor [math]k[/math]. [/size][/size]How would the areas of these 3 cross sections compare? Explain your reasoning.[br]
What does this information about cross sections tell you about the volumes of the 3 solids?[br]
Calculate the volume of each of the solids.
An octahedron is a solid whose faces consist of 8 equilateral triangles.
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[/img][br]Find the volume of an octahedron with edge length [math]\ell[/math].
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Information: IM Geo.5.13 Lesson: Building a Volume Formula for a Pyramid