Rectangular Prism:
Surface area = 2lw + 2lh + 2wh = 2(7)(11) + 2(7)(2) + 2(11)(2) = 154 + 28 + 44 = 226 sq in
Cost of cardboard = 226 sq in × $0.07/sq in = $15.82
Cost per cereal box = $15.82 ÷ 12 boxes = $1.32/box
Rectangular Pyramid:
Surface area = lw + 2[(1/2)l × s] = 6(6) + 2[(1/2)(6)(5)] = 36 + 30 = 66 sq in
Cost of cardboard = 66 sq in × $0.07/sq in = $4.62
Cost per cereal box = $4.62 ÷ 12 boxes = $0.39/box
Cylinder:
Surface area = 2πr^2 + 2πrh = 2π(2)^2 + 2π(2)(12) = 8π + 48π = 56π sq in
Cost of cardboard = 56π sq in × $0.07/sq in ≈ $12.40
Cost per cereal box = $12.40 ÷ 12 boxes = $1.03/box
Therefore, the cost of manufacturing each cereal box varies depending on the shape of the box and ranges from $0.39 to $1.32 per box.
Find the cost of manufacturing each cereal box. Cardboard costs $0.07 (7 cents) per square inch. Show all work in the box provided and round answers to nearest hundredth.
Rectangular Prism:
V = 7 in x 11 in x 2 in
V = 154 cubic inches
Rectangular Pyramid:
6 × 6 = 36 sq in
Volume = (1/3) × 36 sq in × 13 in = 156 cubic inches
Cylinder:
πr^2h
= π(2)^2(12)
= 4π(12)
= 48π
≈ 150.8 cubic inches
(This is 10th grade math, please don't make advanced)
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