document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189358>Question 1189358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "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.\r<BR>\n" );
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document.write( "Volume is 432 cm3. </SPAN>\n" );
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document.write( "The given information is inconsistent.  The described regular hexagonal prism does not have a volume of 432 cubic centimeters.<br><BR>\n" );
document.write( "I will ignore that stated volume and work the problem with the given measurements.<br><BR>\n" );
document.write( "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.)<br><BR>\n" );
document.write( "The area of a regular hexagon with side length 4 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%29%28%28%284%5E2%29sqrt%283%29%29%2F4%29 ALIGN=MIDDLE  ALT=\"%286%29%28%28%284%5E2%29sqrt%283%29%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 41.57 to 2 decimal places.  So the combined area of the base and lid is 83.14 cm^2.<br><BR>\n" );
document.write( "The sides of the prism are 6 rectangles each 4cm by 6cm, for a total area of 144 cm^2.<br><BR>\n" );
document.write( "So the total surface area of the prism is 144+83.14=227.14 cm^2.<br><BR>\n" );
document.write( "Multiply that by the cost per square centimeter to find the total cost of the material.<br><BR>\n" );
document.write( "Note that the volume of the box is 6*41.57=249.42 cm^3, not 432 cm^3.<br><BR>\n" );
document.write( "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....<br><BR>\n" );
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