Yes, volume is how much space an object takes up because volume is like mass in a planet, mass pulls you down just as if volume kept the object from going into space.
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No volume is how much space an object takes up. Mass is the measure of the amount of matter in an object.
volume is how much space is in an object (an object with more volume would be bigger) weight is how heavy an object feels due to gravity (an object with more weight would be harder to lift) density is how much matter is in an amount of space (an object with more density would weigh as much as an object with less density but in a smaller space/volume)
volume is how much the object takes up
By definition, volume is the space that an object occupies, or takes up. In Chemistry, volume is often measured in gallons, liters, or milliliters.
It's called displacement. Say you have a closed irregular object. It takes up space. Dunk it in water and it displaces the water. Finding out how much water was displaced tells you how much space the object took up. That's the volume =P.