SOLUTION: 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​ cylinder?

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Question 1119338: 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​ cylinder?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The described smaller cylinder: v=7%2Api%2A4%5E2


The radius doubled cylinder: 7%2Api%2A%284%2A2%29%5E2


How many times larger?

Large cylinder is this much as large as the smaller:
%287pi%2A8%5E2%29%2F%287pi%2A4%5E2%29

%282%5E6%29%2F%282%5E4%29

2%5E2

4

Three times larger than; OR, four times as large as.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The exact measurements are irrelevant.

The formula for the volume of a cylinder is

V+=+%28pi%29%28r%5E2%29%28h%29

Where r is the radius and h is the height.

If the radius is doubled (multiplied by a factor of 2), then the radius squared is multiplied by a factor of 2^2=4.

So the new volume is 4 times the old volume.

But the problem is worded poorly, because it asks "how many times GREATER is the volume of the larger cylinder than the smaller".

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.

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.

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".