Answer: The required ratio of the volumes of two spheres is 125 : 512.
Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.
We are to find the ratio of the volumes of the two spheres.
Let, 'r' and 'R' represents the radii of the two spheres, so
r : R = 5 : 8.
The volume of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Let, V and V' be the volumes of the spheres with radius r and R units respectively.
Then, the ratio of the volumes of the two spheres will be
[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]
Thus, the required ratio of the volumes of two spheres is 125 : 512.
