document.write( "Question 1187070: Packaging is one important feature in producing quality products. A box designer needs to produce a package for a product in the shapes of the pyramid with a square base having a total volume of 200 cubic inches. The height of the package must be 4 inches less than the length of the base. Find the dimension of the product \n" ); document.write( "

Algebra.Com's Answer #818013 by ikleyn(52864) $\"\"$ $\"About$

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\n" ); document.write( "Packaging is one important feature in producing quality products. A box designer needs to produce a package
\n" ); document.write( "for a product in the shapes of the pyramid with a square base having a total volume of 200 cubic inches.
\n" ); document.write( "The height of the package must be 4 inches less than the length of the base. Find the dimension of the product
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document.write( "The \"volume\" equation is\r\n" );
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document.write( "     = 200   cubic inches,\r\n" );
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document.write( "or\r\n" );
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document.write( "     = 600.\r\n" );
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document.write( "One solution can be easily guessed:  x = 10.\r\n" );
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document.write( "Indeed,   =  = 600.\r\n" );
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document.write( "Next, notice that the function   monotonically increases in its domain x > 4.\r\n" );
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document.write( "It means that x = 10  is the UNIQUE solution to the \"volume\" equation, and THERE IS NO other real solution.\r\n" );
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document.write( "ANSWER.  Under given conditions, the unique set of the dimensions of the pyramid is  10 inches for the square base \r\n" );
document.write( "         and  6 inches for the height.\r\n" );
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