So, the ratio of the volumes of the nucleus and the atom is:

$$\frac{V_{nucleus}}{V_{atom}}=\frac{\frac43\pi(A/2)^3}{\frac43\pi(5A/2)^3}=\frac{(1)^3}{(5)^3}=\frac{1}{125}$$

This gives the fraction volume occupied by the nucleus as:

$$\frac{V_{nucleus}}{V_{atom}}=\frac{1}{125}=0.008$$