Volume (physics)
Volume was the amount of space occupied by a three-dimensional object, such as a solid, liquid, gas, or plasma, and was measured by cubic units. 

The volume of a sphere was calculated as "four-thirds  times the  cubed." ()

One's lung capacity could also be determined by knowing the maximum volume of air an individual's lung(s) could hold at any given time. () 

Related calculations based on known volumes include volumetric flow rate, which could be determined by knowing how much volume passed through a specified point during a certain period of time to find cubic kilometers per hour or cubic meters per second. (; ) Additionally, density could be determined by knowing the weight and volume of an object or substance to find gram per cubic centimeter or kilogram per cubic centimeter. ()

Units of volume 
 Barrel / vat
 Cubic foot
 Cubic parsec
 Cubic light year
 
 Gallon
 Gross ton
 Gross vehicle mass
 Metric system
 Milliliter / cubic centimeter / cc (=10-3)
 Centiliter (=10-2)
 Microliter / Cubic millimeter (=10-1)
 Liter (=100)
 Cubic meter (=103)
 Cubic kilometer (=1012)
 Octare
 Pint

Studies 
In 2268, Spock was able to mathematically determine the number of tribbles present aboard Deep Space Station K-7 by, in part, subtracting the amount of grain consumed from the known volume of grain kept in the station's storage compartment. ()

In 2269, the  was on a mission to survey the burnt out supernova Arachna, which required measurements of its radiation and volume expansion. ()

In 2364, the space vessel lifeform that approached Deneb II was measured to be twelve times the volume of the . ()

Later that year, while the Enterprise-D explored the planetoid Vandor IV, the ship's sensors indicated "an immense volume of energy emanating deep within the planet," which was believed to have been harnessed from a nearby pulsar. ()

In 2366, when the Enterprise took on the task of attempting to move the Bre'el IV moon back into its proper orbit, Chief Engineer Geordi La Forge attempted to lighten the load by extending the forward lobe of the warp field to envelop around the moon. He found, however, that the Enterprises field coils were not designed to handle such a large volume. ()

When the Enterprise-D encountered , a spaceborne lifeform the following year, it was calculated in the three hours up to the time the crew was able to determine where to leave it, the creature's total volume had increased by 8.5%. ()

When an infant Changeling was taken under the care of Human-Odo and Doctor Mora Pol in 2373, Odo caught Dr. Mora measuring the Changelings volume. Mora was displeased with the progress the Changeling was making, noting that in a week it had only grown 17%, while during Odo's development in Mora's lab, he was twice the size of this new Changeling in a matter of three days. Odo attributed his faster progress to being "anxious to grow up so I could get out of there." ()

Later that year, during the impended joining of Bajor to the Federation, Quark expected a profitable outcome, with projects of doing five times the volume in sales of root beer alone. ()

In explaining the problems plaguing the planetoid called "The Waters" in 2375, the Monean scientist Riga explained that the ocean was losing containment and that the Hydro-volume had decreased more than 7% in the past year. Later, when it was discovered that "The Waters" was created and held together by a field reactor, that was then malfunctioning, it finally made sense to Riga why the planetoid was experiencing a loss of hydro-volume. ()

External link 
 
Mathematics