The volume of the pyramid and the cone is given by:
[tex]V=\frac{1}{3}Bh[/tex]where B is the area of the base and h is the height.
In this case the volume of pyramid is:
[tex]V=\frac{1}{3}(10)(15)(12)=600[/tex]The volume of the cone is:
[tex]V^{\prime}=\frac{1}{3}\pi(4.5)^2(12)=81\pi[/tex]Therefore the remaining volume is:
[tex]V=600-81\pi=345.5[/tex]Therefore the volume is 345.5 cubic units.
