Main Difference
The main difference between Area and Volume is that the Area is a quantity that expresses the extent of a twodimensional surface or shape, or planar lamina, in the plane and Volume is a quantity of threedimensional space

Area
Area is the quantity that expresses the extent of a twodimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the twodimensional surface of a threedimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the twodimensional analog of the length of a curve (a onedimensional concept) or the volume of a solid (a threedimensional concept).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.
There are several wellknown formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.
Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for twodimensional regions.Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved that such a function exists.

Volume
Volume is the quantity of threedimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straightedged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape’s boundary. Onedimensional figures (such as lines) and twodimensional shapes (such as squares) are assigned zero volume in the threedimensional space.
The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

Area (noun)
A measure of the extent of a surface; it is measured in square units.

Area (noun)
A particular geographic region.

Area (noun)
Any particular extent of surface, especially an empty or unused extent.
“The photo is a little dark in that area.”

Area (noun)
The extent, scope, or range of an object or concept.
“The plans are a bit vague in that area.”

Area (noun)
An open space, below ground level, between the front of a house and the pavement.
“title=The Adventure of the BrucePartington Planspassage=We sprang through into the dark passage, closing the area door behind us.”

Area (noun)
Penalty box; penalty area.

Area (noun)
Genitals.

Volume (noun)
A threedimensional measure of space that comprises a length, a width and a height. It is measured in units of cubic centimeters in metric, cubic inches or cubic feet in English measurement.
“The room is 9x12x8, so its volume is 864 cubic feet.”

Volume (noun)
Strength of sound. Measured in decibels.
“Please turn down the volume on the stereo.”

Volume (noun)
The issues of a periodical over a period of one year.
“I looked at this week’s copy of the magazine. It was volume 23, issue 45.”

Volume (noun)
A bound book.

Volume (noun)
A single book of a publication issued in multibook format, such as an encyclopedia.
“The letter “G” was found in volume 4.”

Volume (noun)
Quantity.
“The volume of ticket sales decreased this week.”

Volume (noun)
The total supply of money in circulation or, less frequently, total amount of credit extended, within a specified national market or worldwide.

Volume (noun)
An accessible storage area with a single file system, typically resident on a single partition of a hard disk.

Volume (verb)
To be conveyed through the air, waft.

Volume (verb)
To cause to move through the air, waft.