document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=740657>Question 740657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of surface areas of two similar cubes is 25:64. Find the volume of the larger cube if the volume of the smaller cube is 1000in^3.\r<BR>\n" );
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document.write( "A. 1600in^3<BR>\n" );
document.write( "B. 2560in^3<BR>\n" );
document.write( "C. 4096in^3<BR>\n" );
document.write( "D. 6400in^3\r<BR>\n" );
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document.write( "I have answered B and been told it's incorrect. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #451660 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=451660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem states that the ratio of surface areas of two similar cubes is 25:64. Find the volume of the larger cube if the volume of the smaller cube is 1000in^3.\r<BR>\n" );
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document.write( "The suface area of a cube is 6a*2, where a is the length of a side.  Then,\r<BR>\n" );
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document.write( "25/64 = 6a^2 / 6b^2  and the ratio reduces to 5/8 = a/b\r<BR>\n" );
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document.write( "The volume of a cube is a^3  where a is the length of a side\r<BR>\n" );
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document.write( "For the smaller cube, we have\r<BR>\n" );
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document.write( "1000 = a^3  and a = 10\r<BR>\n" );
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document.write( "From our ratio we have 5/8 = 10/b and\r<BR>\n" );
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document.write( "5b = 80 and b = 16\r<BR>\n" );
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document.write( "16^3 = 4096 cubic inches which is the volume of the larger cube\r<BR>\n" );
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document.write( "therefore C is the correct choice  </SPAN>\n" );
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