document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206965>Question 1206965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A?<BR>\n" );
document.write( "Give your answer as a percentage. Provide an explanation and proof for your answer. </SPAN>\n" );
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document.write( "The volume of pyramid A is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29%28B%29%28h%29=%281%2F3%29%2814%5E2%29%286%29=2%2A196=392 ALIGN=MIDDLE  ALT=\"V=%281%2F3%29%28B%29%28h%29=%281%2F3%29%2814%5E2%29%286%29=2%2A196=392\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3136%2F392=8 ALIGN=MIDDLE  ALT=\"3136%2F392=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The volume of pyramid B is 8 times AS LARGE AS the volume of pyramid A.<br><BR>\n" );
document.write( "However, the question asks how many times the volume of pyramid B is BIGGER THAN the volume of pyramid A.<br><BR>\n" );
document.write( "Grammatically, 8 times AS LARGE AS is the same as 7 times LARGER THAN; so the grammatically correct answer is 7.<br><BR>\n" );
document.write( "ANSWER: 7 times BIGGER, or 700%<br><BR>\n" );
document.write( "Note: If this problem comes from a textbook or a worksheet, it is very likely that the given correct answer is 8.  However, with the way the question is worded, 8 is not the correct answer.<br><BR>\n" );
document.write( "Unfortunately, in sloppy everyday usage, \"3 times larger than\" and \"3 times as large as\" are used to mean the same thing -- but they do not. \"3 times LARGER THAN\" means the number has GROWN by 300%, which makes it 4 times AS LARGE.<br><BR>\n" );
document.write( "Because of this sloppy everyday usage, NO MATH PROBLEM SHOULD EVER USE A PHRASE LIKE \"3 TIMES LARGER THAN\".<br><BR>\n" );
document.write( "It is almost certain that, when you see that phrase in a math problem, the author of the problem really meant 3 TIMES AS LARGE AS.<br><BR>\n" );
document.write( " </SPAN>\n" );
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