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Big Idea 2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes.

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Presentation on theme: "Big Idea 2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes."— Presentation transcript:

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2 Big Idea 2: Develop an understanding of and use formulas to determine surface areas and volumes of three-dimensional shapes.

3 Benchmarks MA.7.G.2.1: Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2: Use formulas to find surface areas and volume of three-dimensional composite shapes.

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12 Vocabulary The vocabulary can easily be generated from the reference sheet and the Key. This will help you not only to review key vocabulary but the symbols for each word.

13 Vocabulary Take out the vocabulary sheet provided for you and fill in the second column with the definition for each word. – Vocabulary Activity Sheet Vocabulary Activity Sheet Next label the part image in the third column with the letter representing the corresponding vocabulary word. If there is no image draw one.

14 Review Perimeter Use the worksheets to review circumference and Pi – Rolling a circle Rolling a circle – Archemedes estimation of Pi Archemedes estimation of Pi Use the following PowerPoint to review Perimeter – Perimeter PowerPoint Perimeter PowerPoint

15 Review Topics GeoGebra activities for Area of Polygons and Circles Rectangles: – Area of a Rectangle Area of a Rectangle Parallelograms: – Area of a Parallelogram Area of a Parallelogram Triangles: – Area of a Triangle Area of a Triangle

16 Review Topics GeoGebra activities for Area of Polygons and Circles Trapezoids: – Area of a Trapezoid Area of a Trapezoid Circles: – Area of a Circles Area of a Circles

17 Review Composite Shapes PowerPoint for discussing area and perimeter of composite figures. – Composite Shapes PowerPoint Composite Shapes PowerPoint

18 Side 2 Bottom Back Top Side 1 Front Side 2 Bottom Back Top Side 1 Front Length (L) Breadth (B) Height (H) Rectangular Solid GeoGebra for a Cube

19 Bases Do the words Bottom and Base mean the same thing?

20 Base of a 3D Figure Prism: a prism has 2 Bases and the bases, in all but a rectangular prism, are the pair of non- rectangular sides. These sides are congruent, Parallel. Bases Triangular Prism

21 Base of a 3D Figure Bases Cylinder GeoGebra Net for Cylinder

22 Base of a 3D Figure Base Pyramid: There is 1 Base and the Base is the surface that is not a triangle.

23 Base of a 3D Figure Pyramid: In the case of a triangular pyramid all sides are triangles. So the base is typically the side it is resting on, but any surface could be considered the base. Base

24 Net Activity Directions sheet Net Sheets Scissors Tape/glue

25 Building Polyhedra

26 GeoGebra Nets Net of a Cube Net of a Square Pyramid Net of a Cylinder Net of a Cone Net of an Octahedron

27 The net w w w w b h h h h w b b b bb h h h h ? ? ?

28 Total surface Area = Total surface Area w w h b b b h h b x h w x h w x b = 2(b x h) + 2(w x h) + 2(w x b) = 2(b x h + w x h + w x b)

29 Total surface Area

30 Nets of a Cube GeoGebra Net of a Cube

31 Activity: Nets of a Cube Given graph paper draw all possible nets for a cube. Cube Activity Webpage

32 Nets of a Cube

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34 Lateral Area is the surface area excluding the base(s). Lateral Area Net of a Cube

35 Lateral Area Bases Lateral Sides

36 Lateral Area Bases Lateral Surface Net of a cylinder

37 Stations Activity At each station is the image of a 3D object. Find the following information: – Fill in the boxes with the appropriate labels – Write a formula for your surface area – Write a formula for the area of the base(s) – Write a formula for the lateral area

38 Net handouts and visuals Printable nets – – – of_shapes.htm of_shapes.htm – GeoGebra Nets – note note

39 Volume The amount of space occupied by any 3- dimensional object. The number of cubic units needed to fill the space occupied by a solid

40 Volume Activity Grid paper Scissors 1 set of cubes Tape

41 Solid 1

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45 Solids 4 & 5 Circular Base Pentagon Base

46 Volume The number of cubic units needed to fill the space occupied by a solid. 1cm Volume = Base area x height = 1cm 2 x 1cm = 1cm 3

47 Rectangular Prism Volume = Base area x height = (b x w) x h = B x h L L L Total surface area = 2(b x w + w x h + bxh)

48 Comparing Volume h b w When comparing the volume of a Prism and a Pyramid we focus on the ones with the same height and congruent bases. b w h

49 Comparing Volume h b w w b w b h

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52 b w h h b w Volume = B x h = b x w x hVolume = 1/3 (B x h) = 1/3 (b x w x h) Prism Pyramid

53 2(LxB + BxH + LxH) b x w x h Rectangular Solid 6S 2 S3S3 Cube Sample net Total surface area VolumeFigureName

54 Volume formulas Prism and Cylinder – V=B x h Pyramid and Cone – V=1/3 (B x h)

55 Composite figure 8 12


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