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

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

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

CylinderGeoGebra 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

hh

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 b x h

w x h

w x h

w x b

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

BasesLateral 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

Solid 1

Solid 2

Solid 3

Solid 3

Solids 4 & 5

• Circular Base

• Pentagon Base

Volume

• The number of cubic units needed to fill the space occupied by a solid.

1cm1cm

1cm

Volume = Base area x height

= 1cm2 x 1cm

= 1cm3

Rectangular Prism

• Volume = Base area x height= (b x w) x h = B x h

LL

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

bw

w

b

w

b

h

Comparing Volume

h

l

Comparing Volume

h

l

Comparing Volume

b

w

h

h

b

w

Volume = B x h = b x w x h Volume = 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

6S2S3Cube

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

1212

12