The volume of a cube increases by 72.8% after each edge of the cube is scaled by the same factor. By what percent does each edge length…

Volume scales as the cube of the linear scale factor. A 72.8% increase means the new volume is $1.728$ times the old one. If each edge is multiplied by $s$, then $s^3 = 1.728$, so $s = \sqrt[3]{1.728} = 1.2$, because $1.2^3 = 1.728$. An edge factor of 1.2 is a 20% increase, choice C. Choice A (72.8%) wrongly assumes edges increase by the same percent as volume. Choice B (24.3%) comes from dividing 72.8 by 3 and rounding, which is not how cube roots work. Choice D (57.3%) does not follow from any correct step; the cube root is needed, not a square root, which applies to area.