How do you find the volume for a 3-d shape?

Answer 1

It depends on the 3-d shape.

For some shapes, such as pyramids, prisms, parallelepipeds, regular polyhedra, spheres, and ellipsoids there are relatively straightforward formulae. For other 3-d shapes they are not.

In some cases, you can divide up a shape into smaller shapes, each of which falls into one the above category and calculate their volumes.

If the 3-d shape is not soluble in water, you could partly fill a measuring cylinder with water, submerge the shape in it and measure the levels of water in the measuring cylinder before and after introducing the shape. The increase in the apparent volume of water is the volume of the 3-d shape. If the substance of the shape is soluble in water but not some other liquid you could use that liquid.

If you know that the 3-d shape is solid (not hollow), and you know its density, you could measure its mass and then Volume = Mass/Density