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Polyhedrons - Identifying Solids and Calculating Surface Area and Volume

Learn how to identify different polyhedrons, calculate the surface area and volume of cones, prisms, and cylinders, and solve problems related to three-dimensional figures.

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Polyhedrons - Identifying Solids and Calculating Surface Area and Volume

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  1. Splash Screen

  2. Name polygon A by its number of sides. A. pentagon B. heptagon C. octagon D. decagon 5-Minute Check 1

  3. Name polygon B by its number of sides. A. pentagon B. hexagon C. heptagon D. octagon 5-Minute Check 2

  4. Find the perimeter of polygon A. A. 25 cm B. 35 cm C. 40 cm D. 45 cm 5-Minute Check 3

  5. Find the perimeter of polygon B. A. 40 in. B. 42 in. C. 45 in. D. 85 in. 5-Minute Check 4

  6. Classify the polygons as regular or irregular. A. polygon A: regularpolygon B: regular B. polygon A: regularpolygon B: irregular C. polygon A: irregularpolygon B: regular D. polygon A: irregularpolygon B: irregular 5-Minute Check 5

  7. A regular hexagon has a perimeter of 90 meters. What is the length of one side of the hexagon? A. 18 meters B. 10 meters C. 11.25 meters D. 15 meters 5-Minute Check 6

  8. Content Standards G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. Mathematical Practices 2 Reason abstractly and quantitatively. 6 Attend to precision. CCSS

  9. Students will be able • Identify and name three-dimensional figures. • Find surface area and volume. Then/Now

  10. Polyhedron- a solid with all flat surfaces that enclose a single region of space • Face- the flat surface which is a polygon • Edges- the line segments were the faces intersect • Vertex- the point where three or more edges intersect

  11. Polyhedrons (polyhedra) are named by the shape of their bases. Concept

  12. Identify Solids A.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. Example 1

  13. Answer: rectangular prism;Bases: rectangles EFHG, ABDCFaces: rectangles FBDH, EACG, GCDH,EFBA, EFHG, ABDC Vertices: A, B, C, D, E, F, G, H Identify Solids The solid is formed by polygonal faces, so it is a polyhedron. The bases are rectangles. This solid is a rectangular prism. Example 1

  14. Identify Solids B.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. Example 1

  15. 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 Identify Solids The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism. Example 1

  16. Identify Solids C.Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices. Example 1

  17. Identify Solids 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 Example 1

  18. A. Identify the solid. A. triangular pyramid B. pentagonal prism C. rectangular prism D. square pyramid Example 1

  19. B. Identify the solid. A. cone B. cylinder C. pyramid D. polyhedron Example 1

  20. C. Identify the solid. A. triangular prism B. triangular pyramid C. rectangular pyramid D. cone Example 1

  21. Regular polyhedron- a polyhedron if all of its faces are regular congruent polygons and all of the edges are congruent. • Platonic Solids- 5 regular polyhedrons …named because Plato used them extensively Concept

  22. Surface Area- a two dimensional measurement of the surface of a solid figure. It is the sum of the areas of each face. • Volume- the measure of the amount of space enclosed by a solid figure. Concept

  23. π π . Use a calculator. Find Surface Area and Volume Find the surface area and volume of the cone. Example 2

  24. Volume of a cone r = 3, h = 4 Simplify. Use a calculator. Find Surface Area and Volume Answer: The cone has a surface area of about 75.4 cm2 and a volume of about 37.7 cm3. Example 2

  25. Find the surface area and volume of the triangular prism. A. surface area = 288 ft2volume = 336 ft3 B. surface area = 336 ft2volume = 288 ft3 C. surface area = 26 ft2volume = 60 ft3 D. surface area = 488 ft2volume = 122 ft3 Example 2

  26. A. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is inches, and the height is feet. Find theamount of cardboard Mike needs to make the tube. Surface Area and Volume The amount of material used to make the tube would be equivalent to the surface area of the cylinder. Example 3

  27. 399.1 Use a calculator. Surface Area and Volume Surface area of a cylinder r = 1.875 in., h = 32 in. Answer:Mike needs about 399.1 square inches ofcardboard to make the tube. Example 3

  28. B. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is inches, and the height is feet. Find thevolume of the tube. r = 1.875 in., h = 32 in. 353.4 Use a calculator. Surface Area and Volume Volume of a cylinder Example 3

  29. Surface Area and Volume Answer:The volume of the tube is about 353.4 cubic inches. Example 3

  30. A. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the surface area of the box. A. surface area = 2520 in2 B. surface area = 18 in2 C. surface area = 180 in2 D. surface area = 1144 in2 Example 3

  31. B. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the volume of the box. A. volume = 1144 in3 B. volume = 14 in3 C. volume = 2520 in3 D. volume = 3600 in3 Example 3

  32. End of the Lesson

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