The volume of a sphere with radius [tex]r[/tex] is [tex]V=\dfrac43\pi r^3[/tex]. Sphere B has a volume of [tex]64\pi[/tex], so
[tex]V_B=\dfrac43\pi{r_B}^3\implies r_B=\sqrt[3]{\dfrac{64\pi}{\frac43\pi}}=\sqrt[3]{48}[/tex]
Now,
[tex]\dfrac{r_A}{r_B}=\dfrac25\implies r_A=\dfrac{2r_B}5[/tex]
so sphere A has volume
[tex]V_A=\dfrac43\pi\left(\dfrac{2r_B}5\right)^3=\dfrac{512}{125}\pi[/tex]
