Its volume.
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zero. two dimensional figures do not occupk any space
Three dimensional space.
area
That's called the figure's area.That's called the figure's area.That's called the figure's area.That's called the figure's area.
A cone with included interior is 3-dimensional. However, if you are not including the interior it is a 2-dimensional surface residing in a 3-d ambient space. If you're utilizing the common topological definition of dimension, you can derive that a cone (surface only) is 2 dimensional by looking at its open sets.