The volume of a sphere of radius r is given by
[tex]V=\dfrac{4}{3}\pi\cdot r^3[/tex]
For your given conditions, the volume of 1/2 a sphere becomes
[tex]V=\dfrac{1}{2}\cdot\dfrac{4}{3}\cdot\dfrac{22}{7}\cdot 8^3[/tex]
Seems to match your 2nd choice:
... 1 over 24 over 322 over 7(83)
