the area of such an outer part or uppermost layer
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The surface area is the sum of all the shapes' area
increase the surface area of a solid means to increase the area of solid
surface area
There is NO equation for the area of a sphere Assuming you mean surface area, the surface area of a sphere of radius r is 4πr^2.
It would help if the question was less obscure. What do you mean by "work"? How the surface area affects chemical processes (for example the surface area of catalysts), or diffusion, or surface areas and friction?