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1.7 Three-Dimensional Figures

1.7 Three-Dimensional Figures. Objective:Identify and name three-dimensional figures and find surface area and volume of the figures Describe the polyhedron or solid that can be made from a given net including the Platonic Solids.

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1.7 Three-Dimensional Figures

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  1. 1.7 Three-Dimensional Figures Objective:Identify and name three-dimensional figures and find surface area and volume of the figures Describe the polyhedron or solid that can be made from a given net including the Platonic Solids. Extend the study of planar figures to three-dimensions, including the classical solid figures, and develop analysis through cross-sections. Give precise mathematical descriptions or definitions of geometric shapes in the plane and space. , Describe solids and/or surfaces in three-dimensional space when given two-dimensional representations for the surfaces of three-dimensional objects. , Develop and use special formulas relating to polyhedra (e.g., Euler’s Formula).

  2. Polyhedron • Solid with all flat surfaces • Prism • Pyramid • Not Polyhedrons • Cylinder • Cone • Sphere • Named by the Shape of Base

  3. Polyhedron

  4. Is the solid is a polyhedron? Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. rectangular prism; Bases: rectangles EFHG, ABDC Faces: rectangles FBDH, EACG, GCDH,EFBA, EFHG, ABDC Vertices: A, B, C, D, E, F, G, H

  5. Faces: rectangles EFLK, FGML, GHNM, HNOI, IOPJ, JPKE;hexagons EFGHIJ and KLMNOP Vertices:E, F, G, H, I, J, K, L, M, N, O, P Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices hexagonal prism; Bases: hexagon EFGHIJ and hexagon KLMNOP

  6. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices Not a polyhedron

  7. Regular Polyhedron • All sides are regular congruent polygons

  8. Surface Area and Volume Slant Height Height

  9. Example Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is 3 ¾ inches, and the height is 2 2/3 feet. Find the amount of cardboard Mike needs to make the tube. Surface area of a cylinder r = 1.875 in., h = 32 in. A = 399.1 Answer: Mike needs about 399.1 square inches ofcardboard to make the tube.

  10. Assignment • Block Class • Page 71, 6 - 26 even • Extra Credit 1-7 Lab complete problems 1-12, 1 point each on Test

  11. Assignment • Honors Class • Page 71, 12 - 28 every 4th, 32,34,38 • Complete Lab 1.7 problems 2-12 even

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