Its called the surface area, not volume. Volume is inside. You want the outside, like if you wanted to paint it (instead of fill it up). For each 3-D object, there will be a different formula, so I can't help you there. :P
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Just area. Since there is no available term for the sum of the areas of all surfaces of a figure, we call that area of the "irregular" figure.
That's the area.
total surface area
That is called the area.
It is its surface area.