Pressure of lava underneath a volcano

A volcano has just finished erupting, and a pool of molten lava is lying at rest in the crater. The lava has come up through an opening inside the volcano that connects to the earth's molten mantle. The density of the lava is 4.1 g/cm³. What is the pressure in the lava underneath the base of the volcano, 3000 m below the surface of the pool?

ΔP = ρgΔy

= (4.1 g/cm3)(9.8 m/s2)(3000 m)

= (4.1 × 106 g/m3)(9.8 m/s2)(3000 m)

= (4.1 × 103 kg/m3)(9.8 m/s2)(3000 m)

= 1.2 × 108 N/m2

= 1.2 × 108 Pa

This is the difference between the pressure we want to find and atmospheric pressure at the surface. The latter, however, is tiny compared to the ΔP we just calculated, so what we've found is essentially the pressure, P.