Why does cool rock material sink when convection takes place in the mantle

Because cool materials are denser than hot materials; think like warm fronts and cool fronts when warm air rises. It does not contain as much energy as warm materials and therefore cannot be lifted as high, much like a hot air balloon.

Geothermic gradient is the rate of increasing temperature with respect to increasing the depth in the earths interior. away from tech tonic plates boundaries, it is about 25-40 c/km (72-87 degrees f/mi) of depth near the surface in most of the world.

Answer the above statement is correct (true);