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The radius of a wire is decreased to one-third. If the volume is the same, then how much is the length of the wire decreased now?

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9 times

3 times

2 times

10 times

answer is A.

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Detailed Solution

Given that the radius of a wire is decreased to one-third and the volume remains the same.
We have the following formula,
The volume of the cylinder =

π r 2 l

.
Let the new length be L.
Then the volume formula if the radius is one third of the old radius will be,

π 13 r 2 L

Therefore,

π r 2 l = π 13 r 2 × L ⇒ l = 19 L l L = 19

Thus, 9 times decreased wire length.
Therefore the correct option is 1.

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