How is igneous rock formed?
what is the specific name for the rock formed when lava cools and hardens at the earths surface?

Extrusive igneous rocks cool and solidify quicker than intrusive igneous rocks. They are formed by the cooling of molten magma on the earth's surface. The magma, which is brought to the surface through fissures or volcanic eruptions, solidifies at a faster rate.

Igneous rocks are formed when lava cools and hardens.

Igneous rocks are formed when molten rocks (known as magma) from underneath the Earth's surface rise up, cool down and solidify. When the magma solidifies over the surface of Earth, the resulting igneous rocks are known as extrusive rocks.