The difference between using Area and Volume with 2D and 3D figures is that Area is a measure of square units while Volume is a measure of cubic units.
The area of an object is the measure of space occupied by the two-dimensional object (flat) in a plane. Volume on the other hand is the quantity of space occupied by the object, 3-dimensional object in this case. The unit of area is in square units. The unit of volume is in cubic units.
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