What would happen if the valves separating the chambers in a person's heart did not close? the volume of blood pumped from the atria to the body would be reduced because blood would backflow into the ventricles. the volume of blood pumped from the ventricles to the body would increase because blood would flow without restriction from the atria. the volume of blood pumped from the ventricles to the body would be reduced because blood would backflow into the atria. the volume of blood pumped from the atria to the body would increase because blood would flow without restriction from the ventricles.