When two figures are similar, the scale factor is given by the ratio between the measure of two corresponding lengths of the two figures.
[tex]r\propto R\implies R=kr[/tex]
Where k represents the scale factor.
Since the volume is a three dimensional measure(it is the product of three length units), the ratio between the volumes is the scale factor to the third power
[tex]R=kr\implies R^3=(kr)^3=k^3r^3\implies\frac{R^3}{r^3}=k^3[/tex]
Then, in our problem, the ratio between the volumes is:
[tex]\frac{576}{9000}=0.064[/tex]
Then, the scale factor is the cubic root of this ratio:
[tex]\sqrt[3]{0.064}=0.4[/tex]
The scale factor is 0.4.
