Surface area is the area of a given surface. Roughly speaking, it is the "amount" of a surface (i.e., it is proportional
to the amount of paint needed to cover it), and has units of distance squared. Surface
area is commonly denoted
for a surface in three dimensions, or for a region of the plane (in which case it is simply called
"the" area).

For many symmetrical solids, the interesting relationship

(1)

holds between the surface area , volume , and inradius . This relationship can be generalized for an arbitrary convex
polytope by defining the harmonic parameter in place of the inradius (Fjelstad and Ginchev 2003).

Anton, H. Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.Beyer, W. H.
CRC
Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 127-132,
1987.Dorff, M. and Hall, L. "Solids in Whose Area is the Derivative of the Volume." College
Math. J.34, 350-358, 2003.Fjelstad, P. and Ginchev, I. "Volume,
Surface Area, and the Harmonic Mean." Math. Mag.76, 126-129,
2003.Kaplan, W. Advanced
Calculus, 3rd ed. Reading, MA: Addison-Wesley, 1992.