Quick Start Expectations 1.Fill in planner and HWRS HW: F&W p. 16 & 22, #5-7, 23 2.Get a signature on HWRS 3.On desk: journal, HWRS, pencil, calculators, bin 4.Warm Up: Height = 5 cm Width = 10.5 cm Length = 21.5 cm What is the Surface Area of this Kleenex Box? Dimensions: 21.5 cm x 10.5 cm x 5cm

Warm Up Kleenex Box -Dimensions: 21.5 cm x 10.5 cm x 5cm Surface Area: Area of Front face = 21.5 x 5 = Area of Top face = 21.5 x 10.5 = Area of Right fac e = 10.5 x 5 = 52.5 Total Surface Area = 2 ( ) = sq. cm Height = 5 cm Width = 10.5 cm Length = 21.5 cm

What does it mean to be 3-dimensional? Lines are one-dimensional. They only have length. Polygons and circles are 2-dimensional because they have 2 dimensions. Polyhedrons and spheres are 3-dimensional. They have 3 dimensions. Width Length Radius Circumference Width or Length Height Width Length Height

Nets A net is a two-dimensional shape that can be folded into a three-dimensional shape. Examples: Our online tool can help you see how nets fold into rect. prisms.

Surface Area Recap Always label surface area as: units squared or units 2 because surface area only measures two dimensions (length and width). Different ways to solve for surface area: – Solve for the area of all six faces and add them all together. OR – Solve for the area of three of the faces (for example, top, front, and right), add the areas together, and multiply by two (because there are two pairs of faces that are equivalent). OR

Volume Recap Volume is always labeled as: – units cubed or units 3 because we use three dimensions to solve for volume. To find the volume of a polyhedron: – Count how many inch cubes fit in the box. OR – Find the area of the base and multiply it by the height of the polyhedron. Volume = Bh (B = area of base, h = height) OR – Volume of a Rectangular Prism = Length x Width x Height

Use worksheet - Finding the Least Surface Area (8 & 27 cubes)

Find All Possible Arrangements Group Task: – Given 8 cubes find all possible arrangements for a rectangular prism. – Fill in the lab sheet as you are working. – Find the volume for each arrangement. – Find the surface area for each arrangement. – Think about the following: Which arrangement gives you the greatest SA? Which arrangement gives you the least SA?

Possible Arrangements of 8 cubes LengthWidthHeightVolumeSurface Area 8 in1 in 8 in³34 in² 4 in2 in1 in8 in³28 in² 2 in 8 in³24 in² Does it matter which order the dimensions are in? Is (8 in x 1 in x 1 in) the same rectangular prism as (1 in x 1 in x 8 in), or (1 in x 8 in x 1 in) ? Which arrangement had the most surface area? Why? Which arrangement had the least surface area? Why? No! Yes!

Find All Possible Arrangements Group Task: – Find all possible arrangements for 27 cubes. – Fill in the lab sheet as you are working. – Find the volume for each arrangement. – Find the surface area for each arrangement. – Think about the following: Which arrangement gives you the greatest SA? Which arrangement gives you the least SA? – Answer the questions on the back of your lab sheet.

Possible Arrangements of 27 cubes LengthWidthHeightVolumeSurface Area 27 in1 in 27 in³110 in² 9 in3 in1 in27 in³78 in² 3 in 27 in³54 in² Does it matter which order the dimensions are in? Same SA and Volume! No! 27 x 1 x 1 1 x 27 x 1 1 x 1 x 27

Answers to Lab Sheet 1.8 cubes = 2 in x 2 in x 2in 27 cubes = 3 in x 3 in x 3 in 2.The name for these types of prisms is a cube cubes = 2 in x 3 in x 4 in 4.The shape closest to a cube has the least amount of surface area. 5.a. 12 in x 1 in x 1 in will have the most surface area because it is least like a cube. b. 3 in x 2 in x 2 in will have the least surface area because it is most like a cube.

HW: F&W p. 16 & 22, #5-7, 23