Question

4.1.3 Bathu Sneakers have been looking into different shoebox sizes: a large box for male shoes and small box for female shoes. The cost of the cardboard to make the boxes is 0,502 cents/cm². Calculate the percentage savings Bathu Sneakers will make if the smaller box is used compared to the normal larger box. Larger Box Total Surface Area = 4 093 cm² 19 cm 26 cm 34,5 cm Smaller Box Total Surface Area = 3 034 cm² 25 cm 17 cm 26 cm (6)​

Answer 1

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.