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## Surface Area and Volume

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**Surface Area and Volume**Broward County Teacher Quality Grant**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 • 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 • Archemedes estimation of Pi • Use the following PowerPoint to review Perimeter • Perimeter PowerPoint**Review Topics**GeoGebra activities for Area of Polygons and Circles • Rectangles: • Area of a Rectangle • Parallelograms: • Area of a Parallelogram • Triangles: • Area of a Triangle**Review Topics**GeoGebra activities for Area of Polygons and Circles • Trapezoids: • Area of a Trapezoid • Circles: • Area of a Circles**Review Composite Shapes**• PowerPoint for discussing area and perimeter of composite figures. • Composite Shapes PowerPoint**Top**Back Side 2 Side 1 Front Bottom Rectangular Solid Top Back Side 2 Side 1 Front Height (H) Bottom Breadth (B) Length (L) GeoGebra for a Cube**Bases**Do the words Bottom and Base mean the same thing?**Base of a 3D Figure**Bases Triangular Prism 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.**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**Base 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.**Net Activity**Directions sheet Net Sheets Scissors Tape/glue**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 ? h h h w h b b ? b b w h h h h w b b w**Total surface Area**w h w x h w x b b x h b x h b b h h w x h w x b b w + + + + Total surface Area = + = 2(b x h) + 2(w x h) + 2(w x b) = 2(b x h + w x h + w x b)**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**Lateral Area**Lateral Area is the surface area excluding the base(s). Net of a Cube**Lateral Area**Lateral Sides Bases**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.korthalsaltes.com/index.html • http://www.aspexsoftware.com/model_maker_nets_of_shapes.htm • http://www.mathsisfun.com/platonic_solids.html • GeoGebra Nets • http://www.geogebra.org/en/wiki/index.php/User:Knote**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**Solids 4 & 5**Circular Base Pentagon Base**Volume**1cm 1cm 1cm Volume = Base area x height = 1cm2 x 1cm = 1cm3 The number of cubic units needed to fill the space occupied by a solid.**Rectangular Prism**L • Volume = Base area x height = (b x w) x h = B x h L L • Total surface area = 2(b x w + w x h + bxh)**Comparing Volume**When comparing the volume of a Prism and a Pyramid we focus on the ones with the same height and congruent bases. h w b h w b**Comparing Volume**b w h h w w b b**Comparing Volume**h l