The Hawaiian Islands are formed on a region of intra plate volcanic activity on the Pacific plate. This region is known as a hot spot. Scientists are not exactly sure what causes this but they do know that a plume of magma rises through the mantle and forces it's way through the crust to form submarine volcanoes and over time volcanic islands.
The magma that rises here originates from the mantle and not crustal melt and so forms basic or basaltic lava.
The Inca empire was based in Peru. Note that the empire spread in more countries then just the seat of the empire, like Ecuador, Bolivia, Colombia, Chile and Argentina.