I need help with a geometry word problem

Question

A company is deciding which box to use for their merchandise. The first box measures 8 inches by 6.25 inches by 10.5 inches the second box measures 9 inches by 5.5 inches by 11.75 inches.

If each box used materials that cost $0.03 per square inch to make, how much does a company save by choosing to make fifty boxes of the smaller box in comparison to fifty boxes of the larger box 

Answer 1

First, calculate the surface area needed to make each box.

The formula is SA = 2*L*W + 2*W*H + 2*L*H

 

Box 1: 2*8*6.25 + 2*6.25*10.5 + 2*8*10.5

            100 + 131.25 + 168 = 399.25 square inches

 

Box 2: 2*9*5.5 + 2*9*11.75 + 2*5.5*11.75

              99  + 211.5 + 129.25 = 439.75 square inches

 

Difference is 439.75 - 399.25 = 40.5 square inches       I observe that this is approximately 10.1% more

 

Savings is 40.5 * 0.03 = 1.215 or 60.75 for every 50 boxes.

 

I believe that another important factor to consider is the volume of cereal each of these boxes would contain.

 

Box 1: 8*6.25*10.5 = 525 cubic inches

 

Box 2: 9 * 5.5*11.75 = 581.625 cubic inches

 

Now, 581.625 - 525 = 56.625 cubic inches.       I observe that this is approximately 10.8 % more

 

So, the decision to use Box 2, might still be correct.