The volume of the figure will be the volume of the sphere minus the volume of the cylinder. The volume of the sphere will be:
[tex]\begin{gathered} Vs=\frac{4}{3}\pi r^3 \\ where \\ r=10units \\ Vs\approx4186.67units^3 \end{gathered}[/tex]The volume of the cylinder is:
[tex]\begin{gathered} Vc=\pi r^2h \\ where\colon \\ r=4units \\ h=\frac{3}{4}(2\cdot10)=15units \\ so\colon \\ Vc=\pi(4^2)(15) \\ Vc\approx753.6units^3 \end{gathered}[/tex]Therefore, the volume of the figure is:
[tex]\begin{gathered} V=Vs-Vc \\ V=4186.67-753.6 \\ V=3433.07units^3 \end{gathered}[/tex]Answer:
V = 3433.07 units³
