Volumes of Prisms and Pyramids ( Math.Content.6.G.A.2, Math.Content.7.G.A.3, and Math.Content.7.G.B.6) Jessica Damer and Sarah Tackett Lake Shore High School

Real Life Application archive/2012/04/21/horizon-net-wins- the-wiki-ninja-stick-figures-graduate- collection-17-free-images-to- download.aspx 2

Math.Content.6.G.A.2 Math.Content.6.G.A.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume would be the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V= lwh and V=bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Overall Subject Grade Topic Section Common Core State Standards (CCSS) 3

CCSS Continued Math.Content.7.G.A.3 Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids Math.Content.7.G.A.3 Topic Overall Subject Grade Section 4

CCSS Continued Math.Content.7.G.B.6 Solve real-world and mathematical problems involving volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Math.Content.7.G.B.6 Overall Subject Grade Section Topic 5

Prisms Congruent: having the same measure or length Polyhedron: a solid figure with many plane faces Parallel: in this case, two faces that do not intersect Vertices: the intersections of two or more lines Perpendicular: creating a right angle 6

Cubes 15d4b574fb2d All sides, faces, and angles are congruent Each face is a square A=BH 7

Pyramids 72a1e Vertex (AKA vertices)- each point of the polyhedron 8

Cross Sections in Prisms The shape you get when cutting straight through an object Same shape as base of the original polyhedron 9

Cross Sections in Pyramids Same shape as the base Always smaller than the base 10

Cross Sections vs. Height of Pyramids 11

Volume Formula for Prisms V= (A base)(H prism) Area of the base… A=bh =11(5) =55 sq cm Height of prism… 6 cm =55(6) =330 cu cm 12

Another Volume Formula for Prisms V= lwh 13 length width height 11 cm 5 cm 6 cm = 11(5)(6) = 330 cu cm

Volume Formula for Pyramids V= ⅓(A base) (H pyramid) 009/taks_g11_math/11math.htm Area of the base… A=bh =32(32) = 1024 sq in Height of the pyramid… 30 in =⅓(1024)(30) =10240 cu in 14

Why divide by 3? 15

Top Views cubepyramidrectangular prism cylinder sun-teotihuacan-mexico/ photos-top-view-modern-building-image can-top-view.html 16

Front & Side Views cubepyramidrectangular prism cylinder ake-People-Believe-You- Can-Solve-a-Rubik's- Cube-in-Front-of-Them ptian-pyramids-egypt/ n_Building k/p-8134-coca-cola-coke- can.aspx 17

Volume of Cylinders and Prisms V= (Area of the base)(Height of the object) 18 w/purple/octagon-xxl.png

Volume of Cones and Pyramids V= ⅓(Area of base)(Height of the object) 19 w/purple/octagon-xxl.png

Conclusion ●Polyhedrons are used in many different real life situations where one would need to find the volume of it ●A prism’s volume=(Area of the base)(Height of prism) ●A pyramid’s volume=⅓(Area of the base)(Height of the pyramid) ●A pyramid’s volume is one-third the volume of a prism with the same height 20

Works Cited "Cross Sections." Math Is Fun. Web. 5 Feb "Pyramids, Prisms, Cylinders, and Cones." Math Planet. Web. 12 Feb

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