SOLUTION: You have developed a new specialty candy for Dare and have decided to package it using a hexagonal box as shown, with lid and base regular hexagons. Calculate the cost of each pack
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Question 1189358: You have developed a new specialty candy for Dare and have decided to package it using a hexagonal box as shown, with lid and base regular hexagons. Calculate the cost of each package if the material costs $0.07/100cm2.
This is a box in the shape of a hexagonal prism with a height of 6cm and a distance between direct opposite lid corners of 8 cm.
The given information is inconsistent. The described regular hexagonal prism does not have a volume of 432 cubic centimeters.
I will ignore that stated volume and work the problem with the given measurements.
The regular hexagonal base and lid, with 8cm between opposite corners, are regular hexagons with side length 4. (This is easily seen by viewing the hexagon as being composed of 6 equilateral triangles.)
The area of a regular hexagon with side length 4 is = 41.57 to 2 decimal places. So the combined area of the base and lid is 83.14 cm^2.
The sides of the prism are 6 rectangles each 4cm by 6cm, for a total area of 144 cm^2.
So the total surface area of the prism is 144+83.14=227.14 cm^2.
Multiply that by the cost per square centimeter to find the total cost of the material.
Note that the volume of the box is 6*41.57=249.42 cm^3, not 432 cm^3.
Note also that in reality the cost will be more, because a lid just sitting on the top of the open box does not form a usable package....
