Question

find the scale factor of a cube with volume 729m3 to a cube with volume 6859 m3

Answer 1

let's say you have a volume of a cube with side s

volume = s^3

and let's now suppose you scale up each side by some factor k

new volume = (ks)^3 = k^3 * s^3

therefore, if you take new volume/old volume = (k^3 * s^3) / s^3 you get k^3 as the result. taking the cube root of that gives you the scale factor

Answer 2

so, applying this logic to your problem, simply divide the bigger volume/smaller volume and take the cube root of the result to get your scale factor