The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
How to determine the maximum length of each prism?
The surface area of the hexagonal prism is calculated using:
A = 6al + 3[tex]\sqrt[/tex]3 a^2
Where:
a represents the edge length; a = 4 cm
l represents the length (or height) of the prism
The surface area costs $0.04 per square centimeter.
So, we have:
C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]
Divide both sides by 0.04
275 = 24l + 48[tex]\sqrt[/tex]3
Subtract 48[tex]\sqrt[/tex]3 from both sides
24l = 275 - 48[tex]\sqrt[/tex]3
Evaluate the difference
24l = 191.9
Divide both sides by 24
l = 8.0
Hence, the maximum length of each prism is 8.0 cm
Read more about surface areas at:
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