document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119338>Question 1119338</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cylinder with radius 4 inches and height 7 inches has its radius doubled. How many times greater is the volume of the larger cylinder than the smaller&#8203; cylinder? </SPAN>\n" );
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document.write( "The exact measurements are irrelevant.<br><BR>\n" );
document.write( "The formula for the volume of a cylinder is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28pi%29%28r%5E2%29%28h%29 ALIGN=MIDDLE  ALT=\"V+=+%28pi%29%28r%5E2%29%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Where r is the radius and h is the height.<br><BR>\n" );
document.write( "If the radius is doubled (multiplied by a factor of 2), then the radius squared is multiplied by a factor of 2^2=4.<br><BR>\n" );
document.write( "So the new volume is 4 times the old volume.<br><BR>\n" );
document.write( "But the problem is worded poorly, because it asks \"how many times GREATER is the volume of the larger cylinder than the smaller\".<br><BR>\n" );
document.write( "That phrase \"... how many times greater... than...\" should never be used, because the formal, grammatically correct interpretation is different than the sloppy interpretation used in everyday language.<br><BR>\n" );
document.write( "A volume 4 TIMES AS LARGE AS the small cylinder means a volume 3 TIMES LARGER THAN the small cylinder, because \"3 times larger\" than x means x, plus 3 more times x, which is x+3x = 4x.<br><BR>\n" );
document.write( "So the correct answer to the problem that was asked is \"3\"; however I would guess the probability is about 95% that the author of the problem wanted the answer to be \"4\". </SPAN>\n" );
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