Question 932678
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The author of this problem uses improper sloppy language which has no place in a serious math problem.<br>
The other tutor interprets the given statement that the second cylinder is 3 time (sic) longer than the first cylinder to mean that the length of the second cylinder is 3 times the length of the first; and she interprets the statement that the base radus (sic) of the second cylinder is 2 times shorter than the base radius of the first cylinder to mean that the base radius of the second cylinder is 1/2 the base radius of the first cylinder.<br>
Those interpretations are almost surely what the author of the problem intended; however, neither of those interpretations is grammatically correct.  The second statement is in fact total nonsense.<br>
If the length of the first cylinder is x, then the length of the second cylinders is 3x IF IT IS 3 TIMES AS LONG AS the first cylinder.<br>
But if the length of the first cylinder is x and the second cylinder is 3 TIMES LONGER THAN the first, then the length of the second cylinder is x, PLUS 3 more times x -- or x+3x, which is 4x.<br>
So "3 times longer than" means "4 times as long as".<br>
Unfortunately, in sloppy everyday language, "3 times as long as" and "3 times longer than" are used (incorrectly!) to mean the same thing.<br>
The given statement about the radius of the second cylinder is total nonsense.  In everyday language, "2 times shorter than" is sloppily used to mean "1/2 as long as".  But the grammatically correct interpretation of "2 times shorter than" is nonsensical.<br>
If the radius of the first cylinder is y and the radius of the second cylinder is "2 times shorter than" the radius of the first, the correct interpretation of that statement is that the radius of the second cylinder is y, MINUS 2 times y -- which gives y-2y = -y....<br>
A negative number for the radius of the second cylinder is absurd....<br>
Presumably, you have shown the problem exactly how it was given to you, so my comments are not directed to you but rather to the author of the problem.<br>
However, you have the unfortunate task of trying to guess what the given information really means....<br>