Why does a hot air balloon float?

the shape of the balloon prides lift.
the volume of the air displaced by the balloon is less than the volume of the balloon
the weight of the air displaced is less than the volume of the balloon
the weight of the balloon is less than the weight of the air displaced by the balloon

A hot air balloon is a cloth wrap that contains several thousand cubic meters of air inside (a large volume of air). The burner (which is the motor of the balloon and responsible for its elevation) heats the liquid propane to a gaseous state to generate a huge flame, thus heating the air mass inside the balloon. In this way, its density is modified with respect to the air that surrounds it, because the hot air is lighter than the outside air (less dense), causing the balloon to rise and float.

Now, if we know that the density of a body is directly proportional to its mass and inversely proportional to its volume :

We can deduce that

This is proof of Archimedes' Principle:  

A body totally or partially immersed in a fluid at rest, experiences a vertical upward thrust equal to the mass weight of the body volume that is displaced.

In this case the fluid is the air outside. So, the warm air inside the balloon, being less dense, will weigh less than the outside air and therefore will receive an upward pushing force or thrust that will make the balloon ascend.

a small object of mass 3.66 g and charge -17.6 µc is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. what are the magnitude and direction of the electric field?

0.11 m/s and 0.28 m/s should be correct