Question

if the asthenosphere were to cool and become more rigid, how might that affect earths surface? plate movement would slow down or stop, reducing earthquakes and volcanic activity. the crust would melt more quickly, increasing volcanic eruptions. the lithosphere would sink deeper into the mantle. the magnetic field would disappear.

Explanation:

The asthenosphere is a semi - molten layer that allows the lithospheric plates to move. If it cools and becomes more rigid, it would not be able to facilitate plate movement as effectively. Plate movement is responsible for earthquakes and volcanic activity at plate boundaries. A more rigid asthenosphere would slow or stop plate movement, reducing these geological events.
The crust does not melt quickly due to the asthenosphere cooling (the asthenosphere is below the crust). The lithosphere's buoyancy is related to density differences, not just the asthenosphere's rigidity in a way that would make it sink deeper. The magnetic field is generated in the outer core, not related to the asthenosphere's state.

Answer:

Plate movement would slow down or stop, reducing earthquakes and volcanic activity.