Question

If the radius of a wire is decreased to one-fourth of its original and its volume remains the same, then how many times will the new length becomes its original length?

Answer 1

Initial radius is R
length is L
volume of wire = π R²L
now new radius is R - R/4 = 3R/4
new length be L'
new volume = initial volume
⇒π (3R/4)²× L' = π R²L
⇒ (9/16 ) L' = L
⇒L' = 16/9 L
new length is 16/9 times the original length