7. A triangular prism (like the carton of the Toblerone Chocolate) has equilateral triangles as bases and is used to contain a sample of antimatter. If the top and bottom bases are made of Platinum (Platinum Price Per 1 Gram: 30 USD, sheet manufacturing cost per gram: 5 USD, density: 21 g/cm3), and the sides are made of newly discovered precious metal adamantium (Price Per 1 Gram: 50 USD, sheet manufacturing cost per gram: 10 USD, density: 50 g/cm³), Calculate the volume of the largest prism that can be made for Php 1 Million Pesos. The thickness of sheets to manufacture the prism is 1 mm, and 1 USD=55 Php. Assume the thickness of the metal is negligible in comparison to the dimension of the prism.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Can you explain how did the expert derived the volume of the prism, surface area, and the volume of the sheet? Thank you so much. The second picture is the basis of the problem.

7. A triangular prism (like the carton of the Toblerone Chocolate) has equilateral triangles as
bases and is used to contain a sample of antimatter. If the top and bottom bases are made
of Platinum (Platinum Price Per 1 Gram: 30 USD, sheet manufacturing cost per gram: 5
USD, density: 21 g/cm3), and the sides are made of newly discovered precious metal
adamantium (Price Per 1 Gram: 50 USD, sheet manufacturing cost per gram: 10 USD,
density: 50 g/cm³), Calculate the volume of the largest prism that can be made for Php 1
Million Pesos. The thickness of sheets to manufacture the prism is 1 mm, and 1 USD=55
Php. Assume the thickness of the metal is negligible in comparison to the dimension of
the prism.
Transcribed Image Text:7. A triangular prism (like the carton of the Toblerone Chocolate) has equilateral triangles as bases and is used to contain a sample of antimatter. If the top and bottom bases are made of Platinum (Platinum Price Per 1 Gram: 30 USD, sheet manufacturing cost per gram: 5 USD, density: 21 g/cm3), and the sides are made of newly discovered precious metal adamantium (Price Per 1 Gram: 50 USD, sheet manufacturing cost per gram: 10 USD, density: 50 g/cm³), Calculate the volume of the largest prism that can be made for Php 1 Million Pesos. The thickness of sheets to manufacture the prism is 1 mm, and 1 USD=55 Php. Assume the thickness of the metal is negligible in comparison to the dimension of the prism.
Let,
a = Side of the base
1= length of the prism
So, the volume of the prism is,
V = a1
Surface area is,
V3
Surface area =
a² + 3al
The thickness of the sheet =0.1 cm
Now, the volume of the sheet used is,
a + al cm³
20
Transcribed Image Text:Let, a = Side of the base 1= length of the prism So, the volume of the prism is, V = a1 Surface area is, V3 Surface area = a² + 3al The thickness of the sheet =0.1 cm Now, the volume of the sheet used is, a + al cm³ 20
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