Question

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

Answer 1

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$\sqrt$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$\sqrt$3 a^2]

The maximum cost is $11.

So, the equation becomes

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

Substitute 4 for a

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

Evaluate the products and exponents

11 = 0.04 * [24l + 48$\sqrt$3]

Divide both sides by 0.04

275 = 24l + 48$\sqrt$3

Subtract 48$\sqrt$3 from both sides

24l = 275 - 48$\sqrt$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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