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Surface Area

The total area of the exterior surface of a solid. Many formulas for the area of a surface are given below.

For the following tables,
h = height of solid s = slant height P = perimeter or circumference of the base
l = length of solid B = area of the base r = radius of sphere
w = width of solid R = radius of the base a = length of an edge

Figure Volume Lateral Surface Area Area of the Base(s) Total Surface Area
Box (also called rectangular parallelepiped, right rectangular prism) lwh 2lh + 2wh 2lw 2lw + 2lh + 2wh
Prism Bh Ph 2B Ph + 2B
Pyramid - B -
Right Pyramid B
Cylinder Bh - 2B -
Right Cylinder Bh Ph 2B Ph + 2B
Right Circular Cylinder πR2h Rh R2 Rh + 2πR2
Cone - B -
Right Circular Cone πRs or πR2 πRs + πR2 or

Figure Volume Total Surface Area
Sphere
Regular Tetrahedron
Cube (regular hexahedron) a3 6a2
Regular Octahedron
Regular Dodecahedron
Regular Icosahedron

For the tables above,
h = height of solid s = slant height P = perimeter or circumference of the base
l = length of solid B = area of the base r = radius of sphere
w = width of solid R = radius of the base a = length of an edge

 

See also

Lateral surface, right prism, right regular pyramid, frustum of a cone or pyramid, torus, surface area of a surface of revolution

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes