Granite and basalt are the most common types of igneous rock.   Igneous rock types, or classifications, also include those that are intrusive and extrusive.Intrusive igneo … us rock is formed from the solidification of slow cooling magma below the surface.Extrusive igneous rock is formed for the solidification of rapidly cooling lava at or near the surface.12 people found this useful. Alex Buckley.onfidence votes 3. To the people that are doing the Rock Worksheet the answer for problem #5 is in the paper but the answer is actually (what I put), Another name for igneous rocks is the rock of fire..