Home - News ( United States | United Kingdom | Italy | Germany ) - Football scores

Showing content from http://reference.wolfram.com/language/ref/Volume.html below:

Volume—Wolfram Language Documentation

We deliver solutions for the AI era—combining symbolic computation, data-driven insights and deep technology expertise.

• Data & Computational Intelligence
• Model-Based Design
• Algorithm Development
• Wolfram|Alpha for Business
• Blockchain Technology
• Education Technology
• Quantum Computation

WolframConsulting.com

• See Also
  • Area
  • SurfaceArea
  • ArcLength
  • RegionMeasure
  • Perimeter
  • RegionCentroid
  • Integrate
  • NIntegrate
  • RegionBoundary
• Related Guides
  • Region Properties and Measures
  • Vector Analysis
  • Solid Geometry
  • Polyhedra
  • 3D Printing
  • Calculus
  • Precollege Education

Volume[reg]

gives the volume of the three-dimensional region reg.

Volume[{x₁,…,x_n},{s,s_min,s_max},{t,t_min,t_max},{u,u_min,u_max}]

gives the volume of the parametrized region whose Cartesian coordinates x_i are functions of s, t, u.

Volume[{x₁,…,x_n},{s,s_min,s_max},{t,t_min,t_max},{u,u_min,u_max},chart]

interprets the x_i as coordinates in the specified coordinate chart.

• A three-dimensional region can be embedded in any dimension greater than or equal to three.
• In Volume[x,{s,s_min,s_max},{t,t_min,t_max},{u,u_min,u_max}], if x is a scalar, Volume returns the volume of the parametric three-region {s,t,u,x}.
• Coordinate charts in the fifth argument of Volume 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:
• Symbolic limits of integration are assumed to be real and ordered. Symbolic coordinate chart parameters are assumed to be in range given by the "ParameterRangeAssumptions" property of CoordinateChartData.

The volume of a unit ball in 3D:

The volume of a standard simplex in 3D:

The volume of a rectangular cuboid:

Volume of the cylinder , expressed in cylindrical coordinates:

The volume of a ball represented as an ImplicitRegion:

A cylinder:

The volume of a ball represented as a ParametricRegion:

A cylinder represented with a rational parametrization:

The volume of an ellipsoid with semimajor axes 3, 2, and 1:

The volume of a hemispherical shell in spherical coordinates:

The volume of a torus of major radius 5 and minor radius 2:

The volume of the product of a disk and a circle embedded in four-dimensional space:

The volume of the paraboloid over the rectangle :

Volume of one octant of a three-sphere using stereographic coordinates:

The area of an elliptic pyramid with arbitrary semimajor axis , semiminor axis , and height :

Adding an assumption that the semiaxes are positive simplifies the answer:

The region for , , and :

Compute the Volume using machine arithmetic:

In some cases, the exact answer cannot be computed:

Find the Volume using 30 digits of precision:

A function region :

The region is a volume:

The volume of the region:

Equivalently:

Compute the volume of a polyhedron:

The shape of the Earth is nearly that of an oblate spheroid with volume:

Substitute in the values for the semimajor and semiminor axes:

Find the mass of methanol in a Ball:

Find the mean density of a Cone with a non-uniform mass density defined by :

Compute the volume of empty space in a can with tennis balls, each with a radius of 1.75 inches:

Visualize a can of three balls:

Volume is a non-negative quantity:

Volume[r] is the same as RegionMeasure[r] for 3D regions:

Volume[r] is the same as RegionMeasure[r,3] in general:

Volume[x,s,t,u,c] is equivalent to RegionMeasure[x,{s,t,u},c]:

For a 3D region, Volume is defined as the integral of 1 over that region:

To get the surface volume of a 4D region, use RegionBoundary:

The parametric form of Volume computes the volume of possibly multiple coverings:

The region version computes the volume of the image:

The volume of a region of dimension other than 3 is Undefined:

RetroSearch is an open source project built by @garambo | Open a GitHub Issue

Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo

HTML: 3.2 | Encoding: UTF-8 | Version: 0.7.4