How do you find the volume of a irregular shaped object?

Answer 1

You use integration. That means you divide it into lots of smaller pieces; for example into thin, parallel slabs. For each slab you calculate the area, and multiply it by the thickness.If the slab has an irregular area, you may need to divide it into many thin strips - so you would basically do a double integration.

Answer 2

The answer, for a moderately sized solid object is by the method of liquid displacement.

Find a liquid in which the object is not soluble. Partially fill a graduated container with that fluid and record the level of the liquid, V0. Then gently introduce the object into the container until it is fully submerged. Shake the container a bit so that any air bubbles on the surface of the object are disloded. Record the level of the liquid, V1. Then the volume of the object is V1 - V0 units.