Rectangular Prism:
- The total surface area of the rectangular prism is:
2(7 x 11) + 2(7 x 2) + 2(11 x 2) = 154 square inches
- The cost of the cardboard for the rectangular prism is:
154 sq in x $0.07/sq in = $10.78
- The volume of the rectangular prism is:
7 in x 11 in x 2 in = 154 cubic inches
- The cost per in3 is:
$10.78/154 in3 ≈ $0.07/in3
Rectangular Pyramid:
- The total surface area of the rectangular pyramid is:
36 sq in + 2(6 x 13) = 96 square inches
- The cost of the cardboard for the rectangular pyramid is:
96 sq in x $0.07/sq in = $6.72
- The volume of the rectangular pyramid is:
(1/3) x 36 sq in x 13 in = 156 cubic inches
- The cost per in3 is:
$6.72/156 in3 ≈ $0.04/in3
Cylinder:
- The total surface area of the cylinder is:
2π(2 x 12) + 2π(2)^2 = 100.53 square inches (rounded to nearest hundredth)
- The cost of the cardboard for the cylinder is:
100.53 sq in x $0.07/sq in = $7.04
- The volume of the cylinder is:
π(2)^2(12) = 150.8 cubic inches
- The cost per in3 is:
$7.04/150.8 in3 ≈ $0.05/in3
Therefore, the cost of manufacturing each cereal box varies depending on the shape of the box, with the rectangular prism being the most expensive at approximately $0.07 per cubic inch, followed by the cylinder at approximately $0.05 per cubic inch, and the rectangular pyramid being the cheapest at approximately $0.04 per cubic inch.
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.
Find the cost per in3
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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1 answer