The density of a material is defined as its mass per unit volume.

In everyday usage, mass is commonly confused with weight. But, in physics and engineering, weight means the
strength of the gravitational pull on the object; that is, how heavy it is, measured in units of newtons. In everyday
situations, the weight of an object is proportional to its mass, which usually makes it unproblematic to use the same
word for both concepts. However, the distinction between mass and weight becomes important for measurements
with a precision better than a few percent (due to slight differences in the strength of the Earth's gravitational field at
different places), and for places far from the surface of the Earth, such as in space or on other planets.

The
volume of any solid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies,
often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as
squares) are assigned zero volume in the three-dimensional space. Volume is presented as mL or cm3 (milliliters or
cubic centimeters).

Volumes of straight-edged and circular shapes are calculated using arithmetic formulas. Volumes of other curved
shapes are calculated using integral calculus, by approximating the given body with a large number of small cubes or
concentric cylindrical shells, and adding the individual volumes of those shapes. The volume of irregularly shaped
objects can be determined by displacement. If an irregularly shaped object is less dense than the fluid, you will need
a weight to attach to the floating object. A sufficient weight will cause the object to sink. The final volume of the
unknown object can be found by subtracting the volume of the attached heavy object and the total fluid volume
displaced.

In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian
invariant.

Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with
contents measured commonly in liters or its derived units), and volume being how much space an object displaces
(commonly measured in cubic meters or its derived units). The volume of a dispersed gas is the capacity of its
container. If more gas is added to a closed container, the container expands (as in a balloon), the pressure inside the
container increases, or both.

Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume
over a specified time period.

Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.

Source: WikepediA