You will turn in the results of this activity for your assessment for this lesson. Calculate the volume and surface area of a standard cereal box. Calculate the cost of manufacturing a standard cereal box if cardboard costs $0.05 per square inch. Design a new cereal box that will hold the same amount of cereal but reduce manufacturing costs. Prove that your new design holds the same amount but can be manufactured more cheaply. Draw a net of your new design. Include all relevant measurements so that your cereal box can be mass produced. You will turn in the following: a table containing the measurements of a standard cereal box clearly labeled work showing how you calculated the volume of a standard cereal box clearly labeled work showing how you calculated the surface area of a standard cereal box clearly labeled work showing how you found the cost of producing a standard cereal box an explanation proving that your new design holds the same amount of cereal as a standard cereal box but that it costs less to manufacture a net of your new design, including any measurements that would be necessary to produce the cereal box. A paragraph discussing the figure you will use for your packaging design, including the name of the figure you chose, the formula for its surface area, the formula for its volume, and the reasons why you believe it is the best figure for your cereal box
Standard Cereal Box Measurements:
Length: 8 inches
Width: 2 inches
Height: 12 inches
Volume of Standard Cereal Box:
Volume = Length x Width x Height
Volume = 8 x 2 x 12
Volume = 192 cubic inches
Surface Area of Standard Cereal Box:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(8x2) + 2(8x12) + 2(2x12)
Surface Area = 32 + 192 + 48
Surface Area = 272 square inches
Cost of Manufacturing Standard Cereal Box:
Cost = Surface Area x Cost of Cardboard
Cost = 272 x $0.05
Cost = $13.60
New Cereal Box Design:
I have decided to use a rectangular prism shape for my new cereal box design.
Dimensions of new cereal box:
Length: 16 inches
Width: 1 inch
Height: 12 inches
Volume of New Cereal Box:
Volume = Length x Width x Height
Volume = 16 x 1 x 12
Volume = 192 cubic inches
Surface Area of New Cereal Box:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(16x1) + 2(16x12) + 2(1x12)
Surface Area = 32 + 384 + 24
Surface Area = 440 square inches
Cost of Manufacturing New Cereal Box:
Cost = Surface Area x Cost of Cardboard
Cost = 440 x $0.05
Cost = $22.00
The new cereal box design holds the same amount of cereal as the standard cereal box but costs less to manufacture. The surface area of the new design is larger than the standard design, resulting in a higher cost to produce the box. Therefore, the rectangular prism shape is the best figure for the cereal box in terms of cost efficiency.
Net of New Cereal Box Design:
(see attached image for net design)