It depends on the shape.
There are relatively straightforward formulae for a sphere, cylinder, cone, prism (including cuboid), pyramid. Less simple formulae for parallelepipeds, ellipsoids and perhaps complex ones for other simple shapes. And then you have seriously complex 3-d shapes (a lump of putty) for which there are virtually no direct formulae.
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Volume
Well it depends on what kind of 3d shape it is. There is a formula to find the volume of each 3d shape. The main formula for volume is Bxh. (Big B multiplied by the height.) Bxh means the area of the base times the height.
The answer will depend on what "it" is.
The 3D space inside a shape is it's volume.
A 2D shape is flat and only has a surface area whereas a 3D shape is an object that has surface area and volume.