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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.
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Continue Learning about Geometry
Why is a circle the odd one out between a circle a cylinder and cone?
A circle is a two-dimensional figure, where the cylinder and cone are three-dimensional.
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