document.write( "Question 1195313: The masses of two similar solids A and B are 20kg and 67.5kg respectively. Given that the surface area of the solid A is 1080cm2 ,calculate the surface area of solid B \n" ); document.write( "

Algebra.Com's Answer #827773 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The masses of two similar solids A and B are 20kg and 67.5kg respectively.
\n" ); document.write( "Given that the surface area of the solid A is 1080cm2 ,calculate the surface area of solid B
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\n" ); document.write( "\n" ); document.write( "            As worded, printed, posted and presented, this problem is INCOMPLETE and, therefore, is INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "            To be correct, it must say, that in addition to geometric similarity, the solids are made of the same material.\r
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\n" ); document.write( "\n" ); document.write( "            So, my solution is for this MODIFIED formulation.\r
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document.write( "If material is the same, then, since its density is the same, the ratio of volumes\r\n" );
document.write( "is the same as the ratio of masses, which is\r\n" );
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document.write( "     = 3.375  times   (the greater to the smaller).\r\n" );
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document.write( "Due to geometric similarity, it implies that the corresponding linear dimensions are in ratio\r\n" );
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document.write( "     = 1.5  times   (the greater to the smaller).\r\n" );
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document.write( "Hence, the ratio of surface areas is the square of the ratio of the corresponding linear dimensions\r\n" );
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document.write( "     =  =  = 2.25.\r\n" );
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document.write( "From this proportion, the surface area of solid B is\r\n" );
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document.write( "     = 1080*2.25 = 2430 cm^2.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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