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Lesson 1-7

Lesson 1-7. Three-Dimensional Figures. Lesson Outline. Five-Minute Check Then & Now and Objectives Vocabulary Key Concept Examples Lesson Checkpoints Summary and Homework. Then and Now. You measured and classified angles. Identify and use special pairs of angles

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Lesson 1-7

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  1. Lesson 1-7 Three-Dimensional Figures

  2. Lesson Outline • Five-Minute Check • Then & Now and Objectives • Vocabulary • Key Concept • Examples • Lesson Checkpoints • Summary and Homework

  3. Then and Now You measured and classified angles. • Identify and use special pairs of angles • Identify perpendicular lines

  4. Objectives • Identify and name three-dimensional figures • Find surface area and volume

  5. Vocabulary • Polyhedron – a solid with all flat surfaces that enclose a single region of space • Face – a flat surface of a polyhedron • Edge – line segments where faces intersect • Vertex – a point where three or more edges intersect • Base – parallel faces in a prism • Surface area – two-dimensional measurement of the surface of a solid figure • Volume – the measure of the amount of space enclosed by a solid figure

  6. Vocabulary • Platonic solid – the five types of regular polyhedrons • Prism – a solid with two parallel congruent faces connected by parallelogram faces • Cylinder – a solid with congruent parallel circular bases connected by a curved surface • Cone – a solid with a circular base connected by a curved surface to a single vertex • Pyramid – a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex • Sphere – a set of points in space that are the same distance from a given point • Regular polyhedron – all of its faces are regular congruent polygons and all edges are congruent

  7. 3-D Introduction • Review of figures introduced in grade school Geometry • Covered in detail in Chapter 12 • Formulas on formula sheet

  8. Key Concept • 3-d polygon • Curved surface

  9. Answer:rectangular prism; Bases: rectangles EFHG, ABDCFaces: rectangles FBDH, EACG, GCDH,EFBA, EFHG, ABDC Vertices: A, B, C, D, E, F, G, H Example 1A Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. The solid is formed by polygonal faces, so it is a polyhedron. The bases are rectangles. This solid is a rectangular prism.

  10. Answer: hexagonal prism;Bases: hexagon EFGHIJ and hexagon KLMNOP 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 Example 1B Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism.

  11. Example 1C C.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. The solid has a curved surface, so it is not a polyhedron. The base is a circle and there is one vertex. So, it is a cone. Answer:Base: circle TVertex:Wno faces or edges

  12. Key Concept • Most of these are not seen in HS Geometry • cube is seen alot • Formulas on formula sheet for ones we need

  13. Key Concept • Formulas on formula sheet for all of these

  14. Example 2 Find the surface area and volume of the cone. Surface area of a cone SA = rl + r² SA = (3)(5)+ (3)² r = 3, l = 5 SA = 24 Simplify SA  75.4 cm² Use a calculator.

  15. Example 2 cont Find the surface area and volume of the cone. Volume of a cone r = 3, h = 4 V = 12 Simplify. V 37.7 cm³ Use a calculator. Answer:The cone has a surface area of about 75.4 cm2 and a volume of about 37.7 cm3.

  16. Example 3A A. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters and architectural plans. The diameter of the base is 3.75 inches, and the height is 2.67 feet. Find the amount of cardboard Mike needs to make the tube. The amount of material used to make the tube would be equivalent to the surface area of the cylinder. Surface area of a cylinder SA = 2rh + 2r² SA = 2(1.875)(32) + 2(1.875)² r = 1.875 in., h = 32 in. SA  399.1 in² Use a calculator. Answer:Mike needs about 399.1 square inches ofcardboard to make the tube.

  17. V ≈ 353.4 Use a calculator. Example 3B B. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters and architectural plans. The diameter of the base is 3.75 inches, and the height is 2.67 feet. Find the volume of the tube. V = πr²h V = π(1.875)²(32) r = 1.875 in., h = 32 in. Answer:The volume of the tube is about 353.4 cubic inches.

  18. Lesson Checkpoints

  19. Summary & Homework • Summary: • Most three-dimensional figures have bases, faces, edges, and vertices (corners) • Many three-dimensional figures are named for their bases • The surface area of a three-dimensional figures can be determined by formulas on the formula sheet • The volume of a three-dimensional figures can be determined by formulas on the formula sheet • Homework: • pg 70-3: 18-23

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