If the radius of a wire is reduced to one-third of its original size while keeping the volume constant, by what factor will its length change?

Explanation

Since the volume of the wire remains constant, and volume is proportional to the cross-sectional area times length, reducing the radius to one-third decreases the cross-sectional area by a factor of (1/3)^2 = 1/9. To maintain the same volume, the length must increase by a factor of 9.