Shawna wants to find a carton large enough to hold 12 plastic shoe boxes that measure 14 inches long by 5 inches high by 6 inche
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The maximum length of the prism is highest length of the hexagonal prism
The maximum length of each prism is 8.0 cm
<h3>How to determine the maximum length of each prism?</h3>The surface area of the hexagonal prism is calculated using:
A = 6al + 33 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 + 33 a^2]
The maximum cost is $11.
So, the equation becomes
11 = 0.04 * [6al + 33 a^2]
Substitute 4 for a
11 = 0.04 * [6 * 4l + 33 * 4^2]
Evaluate the products and exponents
11 = 0.04 * [24l + 483]
Divide both sides by 0.04
275 = 24l + 483
Subtract 483 from both sides
24l = 275 - 483
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
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