Question

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

Answer 1

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.