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All depends on what you are trying to measure. Could be as simple as a tape measure/ruler where you measure 3 along 3 axes (sides) for a simple shape to a sophisticaled, calibrated laser surveying. Which ever way, it is achieved in the same way(mostly), which is measuring lengths of the object (along certain axes(as in the plural of axis, wiki cartesian coordinates if you are interested to give you some insight). Afte the lengths have been found a volume can be found. For complicated shape this has to be broken up in to smaller achievable pieces, (even most of the very sophisicated technology does this)

Alternatively if if it is to find the defining equation of the planes, it is possible to derive the volume of the object using calculus.

another option is if you are measuring a fluid you can drop something of known volume and measure the displace,ment of the fluid and that would allow you to calculate the volume

another option is ultrasonics for instance ultrasonic electromagnetic readiation is basically bounced through a material (for example a metal) and you measure the time it takes to propogate through the material,and if you know the density of the material and the length that is basically enough to be able to calculate volume also.

either way it really depends on what you are trying to measure.

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