[tex]\pi r^{2} \frac{h}{3}[/tex] is the volume of a cone.
the volume of the cone is [tex]27 \pi[/tex]
[tex]\pi r^{2} h[/tex] is the volume of a cylinder
the volume of the cylinder is [tex]81 \pi[/tex]
[tex]81 \pi - 27 \pi = 54 \pi [/tex] which is the volume of the shaded region
