Answer:
- proposed design uses less cardboard, also has less volume. I don't dig it.
- BOXer B has the greatest surface area
- BOXer D has the greatest surface area
Explanation:
When there are many instances of the same calculation, it is convenient to let a spreadsheet or graphing calculator do them. The formula can be entered once and used many times. See the attachment for an example.
1. The surface area of a box with dimensions L, W, D can be written as ...
S = 2(LW +LD +WD) = 2(LW +D(L+W))
Then the surface area of the left (original) box is ...
S = 2(2·12 + 8(2+12)) = 2(24 +112) = 272 . . . . square inches
The surface area of the right (proposed) box is ...
S = 2(4·3 +14(4+3)) = 2(12 +98) = 220 . . . . square inches
The volume of the original box, at 2·12·8 = 192 in³ is greater than the volume of the proposed box (3·4·14 = 168 in³), so the customer gets less cereal with the redesigned box. I don't dig it.
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2. The previous question shows the formula and an example of the calculation. The attachment shows the numbers for this question.
- box A: 62 ft²
- box B: 70 ft² — winner
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3. The attachment shows the numbers for this question.
- box C: 270 m²
- box D: 272 m² — winner