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
SHOW ALL WORK
(This is 10th grade math, please don't make advanced)
Rectangular Prism:
Volume:
V = 7 in x 11 in x 2 in
V = 154 cubic inches
Surface Area:
SA = 2(7 in x 2 in) + 2(7 in x 11 in) + 2(2 in x 11 in)
SA = 28 in² + 154 in² + 44 in²
SA = 226 in²
Rectangular Pyramid:
Volume:
6 × 6 = 36 sq in
Volume = (1/3) × 36 sq in × 13 in = 156 cubic inches
Surface Area:
Area of each triangular face = (1/2) × 6 in × 13.3 in = 39.9 sq in
Surface area = (4 × 39.9 sq in) + 36 sq in = 174.6 sq in
Cylinder:
Volume:
πr^2h
= π(2)^2(12)
= 4π(12)
= 48π
≈ 150.8 cubic inches
Surface Area:
2πr^2 + 2πrh
= 2π(2)^2 + 2π(2)(12)
= 8π + 48π
= 56π
≈ 175.9 square inches
AAAaannndd the bot gets it wrong yet again!
to get the cost of a box, multiply the surface area by 7¢ per in^2
the volume of cardboard is not involved!
I apologize for the previous mistake.
The cost of manufacturing each cereal box can be found by multiplying the surface area by $0.07 per square inch.
For the rectangular prism, SA = 226 in² and the cost of manufacturing each cereal box is:
226 in² x $0.07/in² = $15.82 per box
For the rectangular pyramid, SA = 174.6 in² and the cost of manufacturing each cereal box is:
174.6 in² x $0.07/in² = $12.22 per box
For the cylinder, SA ≈ 175.9 in² and the cost of manufacturing each cereal box is:
175.9 in² x $0.07/in² = $12.32 per box
Therefore, the cost of manufacturing each cereal box varies depending on the shape of the box - from approximately $12.22 to $15.82 per box.
To find the cost per cubic inch, we need to divide the cost of the cardboard by the total volume for each shape.
For the Rectangular Prism:
Cost per cubic inch = Cost of cardboard / Volume
Cost per cubic inch = $0.07 / 154 cubic inches
Cost per cubic inch ≈ $0.00045
For the Rectangular Pyramid:
Cost per cubic inch = Cost of cardboard / Volume
Cost per cubic inch = $0.07 / 156 cubic inches
Cost per cubic inch ≈ $0.00045
For the Cylinder:
Cost per cubic inch = Cost of cardboard / Volume
Cost per cubic inch = $0.07 / 150.8 cubic inches
Cost per cubic inch ≈ $0.00046
Therefore, the cost per cubic inch for each shape is approximately:
Rectangular Prism: $0.00045
Rectangular Pyramid: $0.00045
Cylinder: $0.00046
To find the cost per cubic inch for each of the shapes, we need to multiply the volume of each shape by the cost per square inch of cardboard.
For the Rectangular Prism:
Volume: V = 7 in x 11 in x 2 in = 154 cubic inches
Cost of cardboard per square inch: $0.07
Cost per cubic inch = Volume x Cost per square inch
Cost per cubic inch = 154 cubic inches x $0.07
Cost per cubic inch = $10.78
For the Rectangular Pyramid:
Volume: V = (1/3) x 36 sq in x 13 in = 156 cubic inches
Cost of cardboard per square inch: $0.07
Cost per cubic inch = Volume x Cost per square inch
Cost per cubic inch = 156 cubic inches x $0.07
Cost per cubic inch = $10.92
For the Cylinder:
Volume: V = 48π cubic inches (rounded to the nearest hundredth)
Cost of cardboard per square inch: $0.07
Cost per cubic inch = Volume x Cost per square inch
Cost per cubic inch = 48π cubic inches x $0.07
Cost per cubic inch ≈ $10.33
Therefore, the cost per cubic inch for the Rectangular Prism is $10.78, for the Rectangular Pyramid is $10.92, and for the Cylinder is approximately $10.33.
Cost per in³ for Rectangular Prism:
$0.07 / 154 in³ = $0.00045 per in³
Cost per in³ for Rectangular Pyramid:
$0.07 / 156 in³ = $0.00045 per in³
Cost per in³ for Cylinder:
$0.07 / 150.8 in³ = $0.00046 per in³
Therefore, the cost of manufacturing each cereal box is approximately $0.00045 to $0.00046 per cubic inch, depending on the shape of the box.