document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935773>Question 935773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the ratio of the volumes of two similar rectangular prisms is 125:64. What is the ratio of their base areas? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569119 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the volume of a rectangular prism is area of the base * the height.\r<BR>\n" );
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document.write( "the base is equal to length * width.\r<BR>\n" );
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document.write( "the formula for the volume of a rectangular prism becomes length * width * height.\r<BR>\n" );
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document.write( "the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.\r<BR>\n" );
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document.write( "so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.\r<BR>\n" );
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document.write( "since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.\r<BR>\n" );
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document.write( "the ratio of the base area becomes 25/16.\r<BR>\n" );
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document.write( "to confirm, use an example:\r<BR>\n" );
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document.write( "original prism has dimensions as shown below:<BR>\n" );
document.write( "length = 20<BR>\n" );
document.write( "width = 40<BR>\n" );
document.write( "height = 60<BR>\n" );
document.write( "volume = 20 * 40 * 60 = 48000<BR>\n" );
document.write( "base area = 20 * 40 = 800\r<BR>\n" );
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document.write( "prims that has sides in a ratio of 5/4 to original prism is shown below:<BR>\n" );
document.write( "length = 20 * 5/4 = 25<BR>\n" );
document.write( "width = 40 * 5/4 = 50<BR>\n" );
document.write( "height = 60 * 5/4 = 75<BR>\n" );
document.write( "volume = 25 * 50 * 75 = 93750<BR>\n" );
document.write( "base area = 25 * 50 = 1250\r<BR>\n" );
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document.write( "ratio of the volumes = 93750 / 48000 = 1.953125<BR>\n" );
document.write( "ratio of the base areas = 1250 / 800 = 1.5625\r<BR>\n" );
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document.write( "125/64 = 1.953125<BR>\n" );
document.write( "25/16 = 1.5625\r<BR>\n" );
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document.write( "the formulas work.\r<BR>\n" );
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document.write( "the ratio of the volume is 125/64<BR>\n" );
document.write( "the ratio of the base area is 25/16\r<BR>\n" );
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document.write( " </SPAN>\n" );
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