Volume is used to measure the space of three-dimensional objects by multiplying their length, width, and height. It is used to measure the space which a particular mass occupies. Since volume is usually calculated with parameters such as length, width, and height, this explains why the volume of one-dimensional or two-dimensional objects is usually zero.
The volume of an object is usually measured in cubic centimeters (cm³), cubic meters (m³), milliliters (mL) or liters. On the other hand, the area is used to measure the extent of a surface, most especially for 2-d objects. Since we know that area is a two-dimensional measure of the extent of a surface, its units usually depend on the parameters used in calculating it.
The common units of area are square kilometers (km²), square meter m², square foot (ft²), etc. While you will always need two variables to calculate the area of an object, there is an exception where you will need three variables, especially when calculating surface areas of objects.