sphere - segment volume

The Volume of Sphere Segment or Frustum calculator Sphere Slice/Segment/Frustum computes the volume of the section of a sphere made by two parallel planes cutting through the sphere. 

INSTRUCTIONS: Choose units and enter the following:

• (r₁)  Radius the circle defining the top slice of the sphere.
• (r₂)  Radius the circle defining the bottom slice of the sphere.
• (h)  Height of the segment (frustum) of the sphere or the distance between the two planes

Volume of a Sphere Segment (V): The calculator returns the volume in cubic meters.  However, this can be automatically converted to other volume units (e.g. cup, gallons, liters or cubic feet) via the pull-down menu.

The Math

 A sphere slice or segment could be considered a sphere frustum.  The inputs are upper radius (r₁), lower radius (r₂) and the distance between (h).  The assumption is that both slices are in parallel planes. (See diagram)

The formula for the segment or slice of a sphere is as follows:

             `V = pi*h/6 * ( 3*r_1^2 +3*r_2^2 +  h^2)`

The volume of sphere segment is also known as:

• Volume of a Sphere Slice 
• Volume of a Sphere Frustum 
• Volume of a Sphere Segment 

Sphere Calculators

• Sphere Surface Area based radius (r)
• Sphere Surface Area from Volume
• Sphere Volume from Radius
• Sphere Volume from Circumference
• Sphere Volume from Surface Area
• Sphere Volume from Mass and Density
• Sphere Radius from Volume
• Sphere Radius from Surface Area
• Sphere Weight (Mass) from volume and density
• Sphere Density
• Area of Triangle on a Sphere
• Distance between Two Points on a Sphere
• Sphere Cap Surface Area
• Sphere Cap Volume
• Sphere Cap Weight (Mass) 
• Sphere Segment Volume
• Sphere Segment Weight (Mass)
• Sphere Segment Wall Surface Area (without the circular top and bottom ends)
• Sphere Segment Full Surface Area  (with the top and bottom circles, aka ends)
• Volume of Spherical Shell
• Mass of Spherical Shell

Uses

Many manufactured objects are in the shape of a Sphere Frustum (aka Sphere Segment).  However, the volume of an apple  can be estimated using this formula.

Volume is a three dimensional measurement of the amount of space taken up by an object.  Volume units are cubic measurements for solid objects such as cubic inches and cubic meters.  Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel. 

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape.  Many such calculations are available in the following list of calculators. 

In many cases, the calculators are for a column with a geometric shaped base and vertical sides.  One basic formula for volume is area times a Height when the volume has vertical sides.

Volume Calculators

• Volume from Area and Height
• Volume of a Cube 
• Volume of a Box
• Volume of a Cone
• Volume of a Cone Frustum
• Volume of a Cylinder
• Volume of a Slanted Cylinder
• Volume of a Semicircle
• Volume of a Triangular 
• Volume of a Quadrilateral 
• Volume of a Pentagon 
• Volume of a Hexagon 
• Volume of a Heptagon
• Volume of a Octagon
• Volume of a Nonagon
• Volume of a Decagon
• Volume of a Hendecagon
• Volume of a Dodecagon
• Volume of a Paraboloid
• Volume of a Polygon based Pyramid
• Volume of a Pyramid Frustum
• Volume of a Sphere
• Volume of a Sphere Cap
• Volume of a Sphere Segment
• Volume of a Sphere Shell
• Volume of a Oblate Spheroid
• Volume of a Ellipsoid
• Volume of a Torus
• Volume of a Bottle
• Volume of a Chamfer
• Gasket Volume