Once easy way is displacement. You can place it in liquid and see how much liquid it displaces. This will be the volume.
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One way would be to get a container into which you could put the rock completely, fill it to the brim with water (without the rock in it), then put the rock in and measure the volume of the water that flowed out.
This would be called a graduated cillender. But the ccs vary in this tool...from 100 to 1000 * * * * * A graduated CYLINDER might be a better choice!
Half fill a graduated glass beaker with water and note the level. Place irregularly shaped object into the beaker. Note the new level. The difference between the two levels is the volume of the object. cw: OK, that method works for objects that don't get wet -- like steel. Tissue paper would not be a good candidate. Also, if the object floats, you have to submerge the object.
It would be hard to find a line of symmetry on a moon, as it is likely to be irregularly shaped.
To find the volume of a cube, just measure one edge, and then take the third power of that number (which is to say, it gets multiplied by itself 3 times, so for an edge that it 2" long, you would have 2 x 2 x 2 = 8 cubic inches). To find the volume of an irregularly shaped object, you need a graduated cylinder. You immerse the object in water, and you observe how far the water level rises in the cylinder. If the object is soluble in water, you might use some other liquid such as cooking oil.