The rock that forms when melted rock from inside the Earth cools and hardens is called igneous rock.

Here's why:

* Igneous comes from the Latin word "ignis", meaning fire.

* Magma is the name for molten rock *inside* the Earth.

* Lava is the name for molten rock that has erupted *onto* the Earth's surface.

* When magma or lava cools and solidifies, it forms igneous rock.

There are two main types of igneous rock:

* Intrusive igneous rock forms when magma cools and solidifies *beneath* the Earth's surface. These rocks often have large crystals because they cool slowly.

* Extrusive igneous rock forms when lava cools and solidifies *on* the Earth's surface. These rocks often have small crystals or no crystals at all because they cool quickly.

Examples of igneous rocks include granite, basalt, obsidian, and pumice.