The volume of a solid object is the three-dimensional
concept of how much 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.
Volumes of straight-edged and circular shapes are
calculated using arithmetic formulae. Volumes of other curved shapes
are calculated using
integral calculus, by approximating the given body with a large
amount 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.