Multiple choice

If the radius of a circular wire is decreased to one-third of its original value and its volume remains the same, then the length of the wire will become

  1. 3 times

  2. 6 times

  3. 9 times

  4. 27 times
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of wire (cylinder) = pi * r^2 * L. If r becomes r/3, then r^2 becomes r^2/9. For the volume to remain constant, L must become 9L.

AI explanation

A circular wire is effectively a cylinder whose volume is pi times radius squared times length. If the radius is reduced to one third, the new squared radius becomes one ninth of the original. To keep the volume identical, the new length must compensate by becoming 9 times the original length.

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