Any size cup?
Weight the empty cup.
Fill it with water.
Measure the weight increase.
Calculate volume from density of water: 350 g increase means 350 mL of water - you'll need to do the math for non-metric examples.
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Go get a measuring cup.
Fill the cylinder with water to a marked point. Then place the rock in the water and measure how much the water level rises. That will give you the amount of volume displaced by the rock and so the volume of the rock.
Put an exact amount of water in a measuring cup. Drop in a golf ball. The increase in water level equals the volume of the golf ball, assuming the ball doesn't float. For example, 200mL before ball. 280ml after ball dropped in. Therefore volume equals 40ml or 40 Cubic Centimeters.
Water Displacement
The water displacement method is typically used to find the volume of an irregular solid. The object is submerged in a known amount of water, and the increase in water volume is measured. This increase in volume is equal to the volume of the irregular solid.