Area and Volume of n-Dimensional Spheres

​
dimension
3
radius
1
symbolicr radius r
symbolic dimension d
surface area = 4π
volume =
4π
3
This Demonstration lets you calculate or see the general formulas of the surface area and volume of an
n
-dimensional sphere.

Details

2D 'spheres' are circles and have circumference and area; spheres of dimensions greater than 3 have content for the hypersurface and hypervolume. The skin of a 4D sphere has volume.

External Links

Ball (Wolfram MathWorld)
Circle (Wolfram MathWorld)
Content (Wolfram MathWorld)
Hypersphere (Wolfram MathWorld)
Hypersurface (Wolfram MathWorld)
Measure Theory (Wolfram MathWorld)
Sphere (Wolfram MathWorld)
Surface Area (Wolfram MathWorld)

Permanent Citation

Jon Kongsvold
​
​"Area and Volume of n-Dimensional Spheres"​
​http://demonstrations.wolfram.com/AreaAndVolumeOfNDimensionalSpheres/​
​Wolfram Demonstrations Project​
​Published: September 28, 2007