# SurfaceArea

SurfaceArea[reg]

gives the surface area of the three-dimensional region reg.

SurfaceArea[{x1,,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax}]

gives the surface area of the parametrized region whose Cartesian coordinates xi are functions of s, t, u.

SurfaceArea[{x1,,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax},chart]

interprets the xi as coordinates in the specified coordinate chart.

# Details and Options • A three-dimensional region can be embedded in any dimension greater than or equal to three.
• • In SurfaceArea[x,{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax}], if x is a scalar, SurfaceArea returns the surface area of the parametric three-region {s,t,u,x}.
• Coordinate charts in the fifth argument of SurfaceArea can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
• The following options can be given:
•  AccuracyGoal Infinity digits of absolute accuracy sought Assumptions \$Assumptions assumptions to make about parameters GenerateConditions Automatic whether to generate conditions on parameters PerformanceGoal \$PerformanceGoal aspects of performance to try to optimize PrecisionGoal Automatic digits of precision sought WorkingPrecision Infinity the precision used in internal computations

# Examples

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## Basic Examples(2)

The surface area of a unit ball in 3D:

 In:= Out= In:= Out= The surface area of a standard simplex in 3D:

 In:= Out= In:= Out= ## Scope(12)

Introduced in 2019
(12.0)