first, we find the volume of cone
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}=\frac{\pi\cdot2^2\cdot6}{3}=\frac{\pi\cdot4\cdot6}{3}=\frac{\pi\cdot24}{3}=8\pi[/tex]
then, we find the volume of the semisphere
[tex]V=\frac{2}{3}\cdot\pi\cdot r^3=\frac{2}{3}\cdot\pi\cdot2^3=\frac{2}{3}\cdot\pi\cdot8=\frac{16}{3}\pi[/tex]
so the volume of figure is:
[tex]V=8\pi+\frac{16}{3}\pi=\frac{40}{3}\pi=\frac{40}{3}(3.14)=\frac{125.6}{3}=41.87[/tex]
answer: 41.87 in^3
