Let's calculate the volume of the cone and the volume of the hemisphere seperatly and then add them. I will be accurate to 2 points after the decimal point.
Hemisphere: V = (2/3)*pi*r^3 = 128*pi/3 = 134.04
If the height of the entire object is 10, and the radius of the hemisphere is 4, then the height of the cone is 10 - 4 = 6.
Cone: V = (1/3)*pi*r^2*h = 32*pi = 100.53
Vcone + Vhemisphere = 134.04 + 100.53 = 234.57