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 FILLING & WRAPPING 1.3 Learning Target: I will determine how to design a box with the least packaging material, given the volume of a box. HW: Finish the FW Investigation 1 Pg. 7 and Correct with the Zaption video: FW 1.3 *WDYE Retake this Thursday, 3/24 in Math Lab Warm-up:

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).

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

You discovered yesterday that 24 blocks can be packaged in different ways that use varying amounts of packaging material. By using less material, a company can save money, reduce waste, and conserve natural resources. Which rectangular arrangement of cubes uses the least amount of packaging material? p. 5

Find All Possible Arrangements Group Task: – Given 8 cubes find all possible arrangements for a rectangular prism. – Fill in the packet 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) ? No! Yes!

Possible Arrangements of 8 cubes LengthWidthHeightVolumeSurface Area 8 in1 in 8 in³34 in² 4 in2 in1 in8 in³28 in² 2 in 8 in³24 in² 1. Which arrangement had the most surface area and used the most packaging material for 8 cubes? 2. Which arrangement had the least surface area and used the least packaging material for 8 cubes? a. What is the name of that prism? 2 in x 2 in x 2 in cube 8 in x 1 in x 1 in

Find All Possible Arrangements Group Task: – Find all possible arrangements for 27 cubes. – Fill in the packet 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? p.6

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 Which arrangement (set of dimensions) used the least packaging material for 27 cubes? a. What is the name of this type of prism? 3 in x 3 in x 3 in cube

4. Without solving for the surface area, how could you tell simply by looking at the dimensions which prism will have the least amount of surface area? 5. The dimensions for a box with 12 unit cubes are listed below. 12 x 1 x 1 4 x 3 x 1 6 x 2 x 13 x 2 x 2 a. Which set of dimensions will require the least amount of material or have the smallest surface area? How do you know? 3 x 2 x 2 Because they are the closest dimensions to a cube. The shape closest to a cube has the least amount of surface area.

FILLING & WRAPPING 1.3 Did I meet my Learning Target? I will determine how to design a box with the least packaging material, given the volume of a box. HW: Finish the FW Investigation 1 Pg. 7 and Correct with the Zaption video: FW 1.3 *Remember: WDYE Retake this Thursday, 3/24 in Math Lab