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

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

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

Net Activity Directions sheet Net Sheets Scissors Tape/glue

Building Polyhedra

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

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

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)

Total surface Area

Nets of a Cube GeoGebra Net of a Cube

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

Nets of a Cube

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

Lateral Area Bases Lateral Sides

Lateral Area Bases Lateral Surface Net of a cylinder

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

Net handouts and visuals Printable nets – http://www.senteacher.org/wk/3dshape.php http://www.senteacher.org/wk/3dshape.php – http://www.korthalsaltes.com/index.html http://www.korthalsaltes.com/index.html – http://www.aspexsoftware.com/model_maker_nets_ of_shapes.htm http://www.aspexsoftware.com/model_maker_nets_ of_shapes.htm – http://www.mathsisfun.com/platonic_solids.html http://www.mathsisfun.com/platonic_solids.html GeoGebra Nets – http://www.geogebra.org/en/wiki/index.php/User:K note http://www.geogebra.org/en/wiki/index.php/User:K note

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

Volume Activity Grid paper Scissors 1 set of cubes Tape

Solid 1

Solid 2

Solid 3

Solids 4 & 5 Circular Base Pentagon Base

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

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)

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

Comparing Volume h b w w b w b h

h l

h l

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

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

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

Composite figure 8 12

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