Subtract from the volume of the top half of the sphere and from volume of cone.
Hope the diagram helps. I am not familiar with any 3-d plot. I recommend you to know the quadric surfaces very well and know transformations.
Let me explain I know that was a cone. First, is a cone along the x-axis (you need to know that from quadric surfaces). But you have a minus in front. Thus, it is an upsidedown cone (remember mirror images are negatives of the function, that is what I mean by a transformation). But you have a 4 in from. Thus you are going to shift the cone 4 units up the z-axis and there you have it.