big idea 2: develop an understanding of and use formulas to determine surface areas and volumes of...
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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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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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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.
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Vocabulary
• Take out the vocabulary sheet printed 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.
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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
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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
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Review Topics
GeoGebra activities for Area of Polygons and Circles
• Trapezoids:– Area of a Trapezoid
• Circles:– Area of a Circles
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Review Composite Shapes
• Gloria Aguirre made an excellent PowerPoint for composite figures.
– Composite Shapes PowerPoint
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Side 2
Bottom
Back
Top
Side 1Front
Side 2
Bottom
Back
Top
Side 1Front
Length (L)Breadth (B)
Height (H)
Rectangular Solid
GeoGebra for a Cube
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Base of a 3D Figure• Prism: There are 2 Bases and the bases are the 2
congruent, Parallel sides
Bases
Triangular Prism
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Base of a 3D Figure
Bases
CylinderGeoGebra Net for Cylinder
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Base of a 3D Figure
Base
• Pyramid: There 1 Base and the Base is the surface that is not a triangle.
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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
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Net Activity
• Directions sheet
• Net Sheets
• Scissors
• Tape/glue
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Building Polyhedra
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GeoGebra Nets
• Net of a Cube
• Net of a Square Pyramid
• Net of a Cylinder
• Net of a Cone
• Net of an Octahedron
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The net
l
l
l
l
b
h
hh
h
l
b
b b bb
h
h
h
h
?
?
?
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Total surface Area = l x h + b x h + l x h + b x h + l x b + l x b
= 2 l x b + 2 b x h + 2 l x h
= 2 ( l x b + l x h + b x h )
Total surface Area
l
l
l
l
b
h
hh
h
l
b
b b bb
h
h
h
h
?
?
?
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Total surface Area
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Nets of a Cube
• GeoGebra Net of a Cube
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Activity: Nets of a Cube
• Given graph paper draw all possible nets for a cube.
• Cube Activity Webpage
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Nets of a Cube
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• Lateral Area is the surface area excluding the base(s).
Lateral Area
Net of a Cube
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Lateral Area
Bases
Lateral Sides
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Lateral Area
BasesLateral Surface
Net of a cylinder
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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
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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
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Volume
• is the amount of space occupied by any 3-dimensional object.
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Volume Activity
• Directions sheet
• Grid paper
• Scissors
• 1 set of cubes
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Solid 1
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Solid 2
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Solid 3
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Solid 4
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Solids 4 & 5
• Triangle Base
• Circular Base
• Pentagon Base
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Volume
• is the amount of space occupied by any 3-dimensional object.
1cm1cm
1cm
Volume = base area x height
= 1cm2 x 1cm
= 1cm3
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Cube
• Volume = Base area x height= (S x S) x S= S3
LL
L
• Total surface area = 2SxS + 2SxS + 2SxS
= 6S2
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2(LxB + BxH + LxH)
LxBxH
Rectangular Solid
6S2S3Cube
Sample net
Total surface area
VolumeFigureName
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