You have half a sphere and a cone...the radius of the sphere is 6/2=3 so
V=(4π3^3)/3/2
V=108π/6
V=18π
For the cone you have:
V=(hπr^2)/3 with r=3 and h=12 so
V=108π/3
V=36π
So the total volume is:
18π+36π
54π in^3
which is approximately..
≈169.646in^3
≈169.6in^3 (to nearest tenth of a cubic inch)