Answer :
The volume of the space between the sphere and cube is equal to the volume of the sphere subtracted from the volume of the cube:
[tex]V_{}=V_{cube}-V_{sphere}[/tex]The volume of a cube is:
[tex]V=s^3[/tex]s is the length of each edge in the cube
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi\cdot r^3[/tex]The diameter of the sphere is equal to the edge of the cube, then, its radiusr is:
[tex]r=\frac{s}{2}[/tex]Then, the volume of the space between the sphere and cube is:
[tex]V=s^3-\frac{4}{3}\pi\cdot(\frac{s}{2})^3[/tex]s is 34 in
[tex]\begin{gathered} V=(34in)^3-\frac{4}{3}\pi\cdot(\frac{34in}{2})^3 \\ \\ V=39304in^3-\frac{4}{3}\pi\cdot(17in)^3 \\ \\ V=39304in^3-\frac{4}{3}\pi\cdot4913in^3 \\ \\ V=39304in^3-\frac{19652\pi}{3}in^3 \\ \\ V\approx18724.47in^3 \end{gathered}[/tex]Then, the approximate volume of the space between the sphere and cube is 18724,47 cubic inches