The surface area is the sum of all the areas of all the shapes that cover the surface of the object.
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That is the definition of the surface area!
A curved surface area can be described as one where the gradient of the normal to the surface changes smoothly from point to point.
Lateral Area is the area of the sides of a solid, not including base.
Total surface are is the sum of the areas of all the sides of a three-dimensional object.
By applying the process of triple integration (calculus) to the definition of a sphere.