Now that you have found the amount of cereal that each type of container would hold (volume) and the cost of manufacturing each box, answer the follow questions. Keep in mind the goal is to choose a container that holds as much cereal as possible while being the cheapest make.
I. Which container is the most cost efficient?
a. Rectangular Prism
b. Rectangular Pyramid
c. Cylinder
Why? Use your calculations from part 2 to justify your answer.
II. Why do you think rectangular prisms are typically used for cereal boxes? Hint: Think about marketing and shipping of the product/
(This is 10th grade math, please don't make advanced)
Rectangular Prism:
Surface Area: 226 in²
Cost to make box:
Cost = 226 sq in x $0.07/sq in = $15.82
Volume: 154 in³
Cost per in³ : $0.07 / 154 in³
= $0.00045
Rectangular Pyramid:
Surface Area: 174.9 in²
Cost to make box:
Cost = 174.6 sq in x $0.07/sq in = $12.22
Volume: 156 in³
Cost per in³ : $0.07 / 156 in³
= $0.00045
Cylinder:
Surface Area: 175.9 in²
Cost to make box:
Cost = 175.9 sq in x $0.07/sq in = $12.32
Volume: 150.8 in³
Cost per in³ : $0.07 / 150.8 in³
= $0.00046
I. The most cost efficient container is the rectangular pyramid. It has the lowest cost to make the box and holds a comparable amount of cereal (slightly more than the rectangular prism and slightly less than the cylinder).
II. Rectangular prisms are typically used for cereal boxes because they are easy to stack and store on shelves. They also have a large flat surface area for marketing and labeling. The rectangular shape is also efficient for shipping and distribution, as it can be easily packed into larger boxes or pallets for transportation.
I. Based on the calculations, both the rectangular prism and the rectangular pyramid have the same cost per cubic inch, which is $0.00045. The cylinder, on the other hand, has a slightly higher cost per cubic inch, which is $0.00046. Therefore, the most cost-efficient container option is the rectangular prism.
II. Rectangular prisms are typically used for cereal boxes because of marketing and shipping considerations.
In terms of marketing, rectangular prisms provide a larger surface area that can be utilized for branding, nutritional information, and attractive designs that can catch the attention of consumers. The shape allows for better visibility on shelves and easier stacking, making the packaging appealing and practical for display.
Regarding shipping, rectangular prisms are easier to stack and store efficiently, maximizing space utilization during transportation. The regular shape and flat surfaces of rectangular prisms make them more stable and less prone to damage during the shipping process, reducing the risk of cereal boxes getting crushed or deformed.
Overall, the rectangular prism offers a balance between cost-efficiency, marketing advantages, and practicality in shipping, making it the preferred choice for cereal packaging.