document.write( "Question 1205448: Hi
\n" ); document.write( "A cuboid has front,side and top faces of areas 10a cm^2 7.5a cm^2 and 3cm^2 respectively. What is the volume of the solid in cm^2.
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Algebra.Com's Answer #842255 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "A cuboid has front side and top faces of areas 10 cm^2, 7.5 cm^2 and 3cm^2, respectively.
\n" ); document.write( "What is the volume of the solid in $\"highlight%28cross%28cm%5E2%29%29\"$ cm^3.
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document.write( "Let x, y, z be three dimensions of the cuboid.\r\n" );
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document.write( "From the condition, we have\r\n" );
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document.write( "    xy = 10   cm^2,    (1)\r\n" );
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document.write( "    yz =  7.5 cm^2,    (2)\r\n" );
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document.write( "    xz =  3   cm^2.    (3)\r\n" );
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document.write( "Multiply equations (1), (2) and (3).  You will get\r\n" );
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document.write( "    x^2*y^2*z^2 = 10*7.5*3 = 225 cm^6.\r\n" );
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document.write( "Thus we have  \r\n" );
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document.write( "     = 225  cm^6.\r\n" );
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document.write( "It gives the volume of the cuboid, after taking square root of both sides\r\n" );
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document.write( "    xyz =  = 15 cm^3.\r\n" );
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document.write( "ANSWER.  The volume of the cuboid is 15 cm^3.\r\n" );
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