Volumes of Prisms and Pyramids Math Content 6

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 https: //class 3 fish. wordpress. com/ http: //blogs. technet. com/b/wikininjas/ archive/2012/04/21/horizon-net-winsthe-wiki-ninja-stick-figures-graduatecollection-17 -free-images-todownload. aspx 2

Common Core State Standards (CCSS) 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. Math. Content. 6. G. A. 2 Overall Subject Grade Topic Section 3

CCSS Continued Math. Content. 7. G. A. 3 Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids Math. Content. 7. G. A. 3 Overall Subject Grade Topic 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 Topic Section 5

Prisms Polyhedron: a solid figure with many plane faces Vertices: the intersections of two or more lines Congruent: having the same measure or length Parallel: in this case, two faces that do not intersect Perpendicular: creating a right angle http: //exchange. smarttech. com/details. html? id=d 0 d 3 a 8 f 1 -734 c-4 b 00 -98 bd-15 d 4 b 574 fb 2 d 6

Cubes All sides, faces, and angles are congruent Each face is a square A=BH http: //exchange. smarttech. com/details. html? id=d 0 d 3 a 8 f 1 -734 c-4 b 00 -98 bd 15 d 4 b 574 fb 2 d 7

Pyramids Vertex (AKA vertices) - each point of the polyhedron http: //exchange. smarttech. com/details. html? id=d 4014632 -13 a 5 -43 be-91 b 572 a 1 e 0673849 8

Cross Sections in Prisms Same shape as base of the original polyhedron The shape you get when cutting straight through an object http: //www. regentsprep. org/regents/math/geometry/gg 2/Prism. Page. htm 9

Cross Sections in Pyramids Same shape as the base Always smaller than the base http: //www. mathsisfun. com/geometry/cross-sections. html 10

Cross Sections vs. Height of Pyramids 11

Volume Formula for Prisms V= (A base)(H prism) =55(6) =330 cu cm Height of prism… 6 cm Area of the base… A=bh =11(5) =55 sq cm http: //www. mathatube. com/area-of-a-rectangular-prism. html 12

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

Volume Formula for Pyramids V= ⅓(A base) (H pyramid) =⅓(1024)(30) =10240 cu in Height of the pyramid… 30 in Area of the base… A=bh =32(32) = 1024 sq in http: //ritter. tea. state. tx. us/student. assessment/resources/online/2 009/taks_g 11_math/11 math. htm 14

Why divide by 3? 15

Top Views cube http: //kuttappi. com/2010/03/09/guess-what-came-in-mail-today/ pyramid http: //archmetronblog. com/the-pyramid-of-thesun-teotihuacan-mexico/ rectangular prism http: //www. dreamstime. com/royalty-free-stockphotos-top-view-modern-building-image 10612118 cylinder http: //pixgood. com/coke-can -top-view. html 16

Front & Side Views cube pyramid rectangular prism http: //www. wikihow. com/M ake-People-Believe-You. Can-Solve-a-Rubik's-Cube -in-Front-of-Them http: //www. boomvisits. com/egy ptian-pyramids-egypt/ http: //en. wikipedia. org/wiki/Heybur n_Building cylinder http: //www. wingyipstore. co. uk /p-8134 -coca-cola-cokecan. aspx 17

Volume of Cylinders and Prisms V= (Area of the base)(Height of the object) http: //www. iconsdb. com/icons/previe w/purple/octagon-xxl. png 18

Volume of Cones and Pyramids V= ⅓(Area of base)(Height of the object) http: //www. iconsdb. com/icons/previe w/purple/octagon-xxl. png 19

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. 2015. <http: //www. mathsisfun. com/geometry/cross-sections. html>. "Pyramids, Prisms, Cylinders, and Cones. " Math Planet. Web. 12 Feb. 2015. <http: //www. mathplanet. com/education/pre-algebra/area-and-volume/pyramids, -prisms, -cylinders-and-cones >. 21

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