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

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:

Parallelepiped:

Simplex in 3D:

Ball:

Ellipsoid:

Cylinder:

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:

Introduced in 2019
 (12.0)