# 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 Automatic the precision used in internal computations

# Examples

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## Basic Examples(2)

The surface area of a unit ball in 3D:

The surface area of a standard simplex in 3D:

## Scope(12)

### Special Regions(7)

Surface area of a Cuboid:

Simplex in 3D:

Ball:

Cone:

### Formula Regions(1)

The surface area of a ball represented as an ImplicitRegion:

A cylinder:

### Mesh Regions(2)

The surface area of a MeshRegion:

The surface area of a BoundaryMeshRegion:

### Derived Regions(2)

The surface area of a RegionIntersection:

The surface area of a TransformedRegion:

Wolfram Research (2019), SurfaceArea, Wolfram Language function, https://reference.wolfram.com/language/ref/SurfaceArea.html.

#### Text

Wolfram Research (2019), SurfaceArea, Wolfram Language function, https://reference.wolfram.com/language/ref/SurfaceArea.html.

#### CMS

Wolfram Language. 2019. "SurfaceArea." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SurfaceArea.html.

#### APA

Wolfram Language. (2019). SurfaceArea. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurfaceArea.html

#### BibTeX

@misc{reference.wolfram_2024_surfacearea, author="Wolfram Research", title="{SurfaceArea}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/SurfaceArea.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_surfacearea, organization={Wolfram Research}, title={SurfaceArea}, year={2019}, url={https://reference.wolfram.com/language/ref/SurfaceArea.html}, note=[Accessed: 14-September-2024 ]}