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Lesson 8.1A: Three Dimensional Objects, Nets, and Cross-Sections

Lesson 8.1A: Three Dimensional Objects, Nets, and Cross-Sections. Objective:   R.4.G.8  Draw, examine, and classify cross-sections of three-dimensional objects. Vocabulary. A polyhedron is a three-dimensional solid with flat surfaces and straight edges.

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Lesson 8.1A: Three Dimensional Objects, Nets, and Cross-Sections

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  1. Lesson 8.1A: Three Dimensional Objects, Nets, and Cross-Sections Objective:   R.4.G.8  Draw, examine, and classify cross-sections of three-dimensional objects

  2. Vocabulary • A polyhedron is a three-dimensional solid with flat surfaces and straight edges. • Each polygon is a face of the polyhedron. • An edge is a segment that is formed by the intersection of two faces. • A vertex is a point where three or more edges intersect. • A net is a two-dimensional pattern that you can fold to form a three-dimensional figure. • One of the simplest such figures is a cube — a polyhedron with six faces, each of which is a square.

  3. Vocabulary • Prisms: polyhedron with 2 congruent and parallel faces called bases. • Pyramid: polyhedron in which 1 face is a polygon and the others are triangles…comes to a point at the top. • Cylinder: 3D figure with 2 congruent & parallel bases that are circles • Cone: has 1 circular base and comes to a point at top

  4. Vocabulary Cross Section: The intersection of a solid and a plane. The result is a polygon.

  5. Identifying a Net

  6. Identifying a Net

  7. Identifying a Net

  8. Drawing a Net Packaging Draw a net for the graham cracker box. Label the net with its dimensions.

  9. Drawing a Net

  10. Cross Sections • A cross section is the shape formed when a plane intersects a 3D figure. • Think of a very thin slice of the solid. • The bases are opposite faces that are parallel and congruent. • To describe the relationship between the plane and the solid, it will be either: • Parallel to the base or • Perpendicular to the base • Cross-Sections can be polygons and circles • Tell the shape it makes when you cut the solid

  11. Parallel Cross Sections

  12. Parallel Cross Sections

  13. Perpendicular Cross Sections

  14. Perpendicular Cross Sections

  15. A plane slices through the cylinder below, parallel to the base. What is the resulting cross-section?

  16. A plane slices through the rectangular prism below, parallel to the base. What is the resulting cross-section?

  17. A plane slices through a cone and the resulting cross section is a triangle. Describe the relationship between the plane and the cone.

  18. 6m 4m Given a cone with a height of 6 m and a radius of 4 m, what is the area of the cross-section if a plane slices the cone perpendicular to the base, through the center?

  19. Find the area of the shaded cross-section of the trangular prism

  20. A plane intersects a sphere 3 inches away from the center of the sphere. The radius of the sphere is 5 inches. What is the area of the cross-section, to the nearest tenth?

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