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Surface Area and Volume

Surface Area and Volume. Chapter 12. Lesson goals. Exploring Solids 12.1. California State Standards. 8, 9: Solve problems involving the surface area and lateral area of geometric solids and COMMIT TO MEMORY THE NECESSARY FORMULAS. Identify Polyhedrons Apply Euler’s Theorem. face. face.

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Surface Area and Volume

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  1. Surface Area and Volume Chapter 12

  2. Lesson goals Exploring Solids12.1 California State Standards 8, 9: Solve problems involving the surface area and lateral area of geometric solids and COMMIT TO MEMORY THE NECESSARY FORMULAS. Identify Polyhedrons Apply Euler’s Theorem

  3. face face definition Plural: polyhedra • Polyhedron A 3-dimensional solid figure formed by polygons. • Faces: the polygons that form the polyhedron • Edges: a line segment formed by the intersection of two faces. • Vertex: the point where 3 or more edges meet. edge vertex

  4. examples • Polyhedra • Prism • Pyramid • Non-Polyhedra • Cylinder • Cone • Sphere

  5. definition • Regular Polyhedron • All faces are congruent regular polygons

  6. definition • Platonic Solids • 5 regular, convex polyhedra • Tetrahedron 4 equilateral triangles • Hexahedron 6 squares • Octahedron 8 equilateral triangles • Dodecahedron 12 regular pentagons • Icosahedron 20 equilateral triangles

  7. tetrahedron 4 faces hexahedron 6 faces (cube) octahedron 8 faces icosahedron 20 faces dodecahedron 12 faces

  8. definition • Cross-section • The intersection of a plane and a solid. The cross section is a square. Describe the cross section.

  9. definition • Cross-section • The intersection of a plane and a solid. The cross section is a circle. Describe the cross section.

  10. theorem Euler’s Theorem The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula

  11. example A polyhedron has 18 edges and 12 vertices. How many faces does it have?

  12. example Find the number of vertices for a polyhedron with 10 faces made from 4 triangles, 1 square, 4 hexagons, and 1 octagon. Each side is shared by two polygons

  13. example A soccer ball is made of 12 pentagons and 20 hexagons. How many vertices does the soccer ball have? Each side is shared by two polygons

  14. back left roof left side right side right roof bottom front Definition • Net • the two-dimensional representation of a three-dimensional figure. What would the polyhedron look like if laid flat?

  15. “label” example What would the cylinder look like laid flat? top bottom Remember: this is called a NET.

  16. Today’s Assignment • p. 723: 6 – 15, 25 – 31, 47 – 49

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