It would be the simplest way to do so.
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You take a graduated cylinder,or anything you can measure water in, and put water in it. You drop the marble in and the change in water height is your volume. For example if the cylinder is filled up to 10ml and after you drop in the marble it goes to 15ml then the marble has a volume of 5ml cubed.
I don't believe there is a way to find the mass of an object knowing only the diameter of the object. If you had the volume, or some other measurements sure. the best bet would be just to weigh it, or find the volume using the principles of displacement.
Length times width times height is how you would normally find the volume of a shape.
You can get marble from a quarry or a stone merchant, you can also sometimes find marble tiles at a tile and ceramic shop.
The easiest way is to get a small measuring cup with fractions of ounces and fill it to the one-ounce mark with water or another suitable liquid. Then drop the marble in and subtract 1 ounce from the new measurement. If you can't find a small measuring cup, use a large one and use more marbles, then divide your results by the number of marbles used. If you can't do that, then somehow measure the diameter of the marble, divide it by 2 to find the radius, and plug it into this formula: (4 . pi . r3) / 3 = volume of sphere. Answer: Obviously the use of a graduated cylinder wuld make the process more accurate than using a measuring cup as it is marked in 1 ml increments. Alternately the marble can be weigher and the indicated mass multiplied by the typical specific gravity of glass (2.58) to give the volume