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Paha777 [63]
2 years ago
10

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

ths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
Mathematics
1 answer:
chubhunter [2.5K]2 years ago
6 0

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 + 3\sqrt3 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\sqrt3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3\sqrt3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3\sqrt3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48\sqrt3]

Divide both sides by 0.04

275 = 24l + 48\sqrt3

Subtract 48\sqrt3 from both sides

24l = 275 - 48\sqrt3

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:

brainly.com/question/6613758

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