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 printed 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.

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 Gloria Aguirre made an excellent PowerPoint for 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

Base of a 3D Figure Prism: There are 2 Bases and the bases are the 2 congruent, Parallel sides Bases Triangular Prism

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

Base of a 3D Figure Base Pyramid: There 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 l l l l b h h h h l b b b bb h h h h ? ? ?

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 h h h l b b b bb h h h h ? ? ?

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

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

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

Volume is the amount of space occupied by any 3- dimensional object.

Volume Activity Directions sheet Grid paper Scissors 1 set of cubes

Solid 1

Solid 2

Solid 3

Solid 4

Solids 4 & 5 Triangle Base Circular Base Pentagon Base

Volume is the amount of space occupied by any 3- dimensional object. 1cm Volume = base area x height = 1cm 2 x 1cm = 1cm 3

Cube Volume = Base area x height = (S x S) x S = S 3 L L L Total surface area = 2SxS + 2SxS + 2SxS = 6S 2

2(LxB + BxH + LxH) LxBxH Rectangular Solid 6S 2 S3S3 Cube Sample net Total surface area VolumeFigureName