Answer:
Solid 1:
T.A. = 2(wl + hl + hw)
T.A. = 2(2 * 8 + 4 * 8 + 4 * 2)
T.A. = 2(16 + 32 + 8)
T.A. = 32 + 64 + 16
T.A. = 96 + 16
T.A. = 112m^2
V = w * h * l
V = 2 * 4 * 8
V = 8 * 8
V = 64m^3
M = 0.003 * 64
M = $0.19
Solid 2:
T.A. = l sqr(l^2 + 4 * h^2) + l^2
T.A. = 6 sqr(6^2 + 4 * 5^2) + 6^2
T.A. = 106m^2
V = 1/3 * b * h
V = 1/3 * 36 * 5
V = 12 * 5
V = 60m^3
M = 0.003 * 60
M = $0.18
Solid 3:
T.A. = (2 * pi * r^2) + (2 * pi * r * h)
T.A. = (2 * pi * 2.5^2) + (2 * pi * 2.5 * 3.5)
T.A. = (2 * pi * 6.25) + (2 * pi * 2.5 * 3.5)
T.A. = 39.27 + 54.98
T.A. = 94.25m^2
V = pi * r^2 * h
V = pi * 2.5^2 * 3.5
V = pi * 6.25 * 3.5
V = pi * 21.88
V = 68.72m^3
M = 0.003 * 68.72
M = $0.21
Solid 4:
T.A. = pi * r^2 + pi * r * sqr(r^2 + h^2)
T.A. = pi * 4^2 + pi * 4 * sqr(4^2 + 6^2)
T.A. = pi * 16 + pi * 4 * sqr(16 + 36)
T.A. = 50.26 + 12.56 * sqr(52)
T.A. = 62.82 * sqr(52)
T.A. = 140.9m^2
V = 1/3 * pi * r^2 * h
V = 1/3 * pi * 4^2 * 6
V = 1/3 * pi * 16 * 6
V = 1/3 * pi * 96
V= pi * 32
V = 100.5m^3
M = 0.003 * 100.5
M = $0.30
Solid 5:
T.A. = 4 * pi * r^2
T.A. = 4 * pi * 2.6^2
T.A. = 4 * pi * 6.76
T.A. = pi * 27.04
T.A. = 84.95m^2
V = 4/3 * pi * r^3
V = 4/3 * pi * 2.6^3
V = 4/3 * pi * 17.576
V = pi * 23.434
V = 73.62m^3
M = 0.003 * 73.62
M = $0.22
Write a paragraph that answers the following questions:
● Do all of the solids hold between 60 and 70 cubic inches?
● Which solid is the most cost efficient (the packaging with the smallest materials cost that holds between 60 and 70 cubic inches)?
● Would the Ark be most cost efficient solid for packaging? Why or why not?
● Which solid would you recommend using? Why?
● Why do you think that God was very specific in the measurements that He gave Noah for the Ark? Be sure to use some of your findings from this project to support your answer.
Of the five shapes, only the rectangular prism, the square pyramid, and the cylinder held between 60 and 70 cubic inches. The square pyramid was the most cost efficient, holding a price of $0.18. A rectangular prism would not be the most efficient shape cost wise, however it would be sufficient to hold the materials. I think I would recommend the rectangular prism for this project, because it is the second most cost efficient and holds a greater volume for use. I think God gave Moses the exact plans needed to perfectly fit all his animals. I think he wanted to prove to Moses his power and knowledge by providing the exact amount needed. In this project I took the measurements and I used them to discover which was best suited to serve the purpose needed, but God already knew and used it as a lesson in faith for Moses.
Step-by-step explanation:
