document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034896>Question 1034896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism. <BR>\n" );
document.write( "which stament is true?<BR>\n" );
document.write( "a)The height of the red prism is one-third the height of the blue prism <BR>\n" );
document.write( "B)The height of the red prism is the same as the height of the blue prism<BR>\n" );
document.write( "C)The height of the red prism is six times the height of the blue prism.<BR>\n" );
document.write( "D)The height of the red prism is three times the height of the blue prism. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649814 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=649814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> volume of the red prism = h1 * B1<BR>\n" );
document.write( "volume of the blue prism = h2 * B2<BR>\n" );
document.write( "area of the base of the red prism = 1/3 * the area of the base of the blue prism.<BR>\n" );
document.write( "you get B2/3.<BR>\n" );
document.write( "volume of the red prism = h1 * B2/3.<BR>\n" );
document.write( "volume of the blue prism is still h2 * B2.<BR>\n" );
document.write( "since the volumes are equal, you get:<BR>\n" );
document.write( "h1 * B2/3 = h2 * B2<BR>\n" );
document.write( "divide both sides of this equation by B2 and you get:<BR>\n" );
document.write( "h1/3 = h2<BR>\n" );
document.write( "multiply both sides of this equation by 3 and you get:<BR>\n" );
document.write( "h1 = 3 * h2.<BR>\n" );
document.write( "if the area of the base of the red prism is 1/3 * the area of the base of the blue prism, then the height of the red prism is 3 times the height of the blue prism.\r<BR>\n" );
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document.write( "this is easy to see if you use numbers.<BR>\n" );
document.write( "any numbers will do.<BR>\n" );
document.write( "assume the height of the blue prism is 6 and the area of the base of the blue prism is 9.<BR>\n" );
document.write( "the volume of the blue prism is therefore 6*9 = 54.<BR>\n" );
document.write( "now assume the area of the base of the red prism is 3.<BR>\n" );
document.write( "that's 1/3 * 9.<BR>\n" );
document.write( "in order for the volume to be the same, the height of the red prism has to be 3 * 6 = 18.<BR>\n" );
document.write( "you get 18*3 = 54.<BR>\n" );
document.write( "6*9 =54<BR>\n" );
document.write( "18*3 = 54<BR>\n" );
document.write( "18 is 3*6<BR>\n" );
document.write( "3 is 9/3\r<BR>\n" );
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document.write( "your solution is selection D.<BR>\n" );
document.write( " </SPAN>\n" );
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