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)
Show all work.
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.
Rectangular Prism:
To find the volume of a rectangular prism, we need to multiply the length (L), width (W), and height (H).
Given:
L = 7 in
W = 11 in
H = 2 in
V = L × W × H
V = 7 in × 11 in × 2 in
V = 154 cubic inches
Rectangular Pyramid:
To find the volume of a rectangular pyramid, we need to find the product of the base area and the height, and then divide the result by 3.
Given:
Base area = 6 in × 6 in = 36 square inches
Height = 13 in
Volume = (1/3) × Base area × Height
Volume = (1/3) × 36 sq in × 13 in
Volume = 156 cubic inches
Cylinder:
To find the volume of a cylinder, we need to use the formula V = πr^2h, where π is approximately equal to 3.14, r is the radius, and h is the height.
Given:
Radius (r) = 2 in
Height (h) = 12 in
Volume = π × r^2 × h
Volume = π × (2 in)^2 × 12 in
Volume ≈ 150.8 cubic inches
Now, to find the cost per cubic inch, we need to divide the cost per square inch by the volume.
Given:
Cost per square inch = $0.07
Cost per cubic inch = Cost per square inch / Volume
Cost per cubic inch = $0.07 / 154 cubic inches (for the rectangular prism)
Cost per cubic inch = $0.07 / 156 cubic inches (for the rectangular pyramid)
Cost per cubic inch = $0.07 / 150.8 cubic inches (for the cylinder)
Round the answers to the nearest hundredth:
Cost per cubic inch for the rectangular prism ≈ $0.00045
Cost per cubic inch for the rectangular pyramid ≈ $0.00045
Cost per cubic inch for the cylinder ≈ $0.00046
Therefore, the cost of manufacturing each cereal box is approximately $0.00045 per cubic inch for the rectangular prism, $0.00045 per cubic inch for the rectangular pyramid, and $0.00046 per cubic inch for the cylinder.