Question

Many people are surprised to find that math is found in the Bible in many places. God created all things and sustains all things. That includes math and shapes. In fact, the owner of a candy company has always been in awe of Noah’s Ark and how God instructed Noah to build it using very specific instructions. Noah's instructions were given to him by God in Genesis 6:15: “This is how you are to build it: The ark is to be 300 cubits long, 50 cubits wide and 30 cubits high.” The owner of the company knows that building an exact replica of Noah’s Ark may be difficult. Therefore, he would like to simplify things by assuming the ark is the shape of a rectangular prism. While the owner would really like to make his candy container in the shape of a rectangular prism to be able to closely model Noah’s Ark, he isn’t sure that solid shape will be the most efficient one for packaging the product.
He has hired you as their new production manager. Your job is to look at five different solid figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the five options shown below. The candy is animal gummies. The package must hold between 60 and 70 cubic inches (roughly 4-5 cups of space). The cost of the plastic for the packaging is $0.003 per square inch.

Your project should include the volume, total surface area, and materials cost for each solid given below, including the formulas you used and each step of your work. Be sure to find all measures for each solid, even if the solid does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.

You also need to include 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.

Answer 1

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: