Sphere Segment Weight

The Mass or Weight of a Sphere Segment Weight calculator computes the weight or mass of a slice of a sphere.     Sphere Segment 

INSTRUCTIONS: Choose units and enter the following:

• (r₁)  Radius of Top of Sphere
• (r₂)  Radius of Bottom of Sphere
• (h)  Height of Sphere Segment (the distance between the two planes)
• (mD) Density of Material.(Default: 7,850 kg/m³ for steel)

Mass or Weight of a Sphere Segment (m): The calculator returns the mass in grams.  However, this can be automatically converted to other mass or weight units (e.g. pounds, tons) via the pull-down menu.

The Math / Science

A sphere slice or segment could be considered the frustum of a sphere.  The inputs are upper radius, lower radius, the distance between and the density.  The assumption is that both slices are in parallel planes. (See diagram)  The volume is calculated and then the weight/mass is calculated using a mean density (mD) of the substance of the slice.

This formula computes the volume of segment or slice of a sphere as follows:

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

With the volume, this formula then executes the simple mass equation below to compute the approximate mass of the object.

             m = mD * V

Mean Density Table

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

• kilograms per cubic meter (kg/m³)
• grams per cubic centimeter (g/cm³)
• grams per liter (g/L)
• pounds per cubic feet (lb/ft³)
• ounces per cubic inch (oz/in³)
• pounds per barrel (lb/bbl)
• pounds per bushel (lb/bu)

If you want to identify a material by its density, use the Density Within Range tool.

Weight is technically the downward force that a mass exerts based on the force of gravity and the mass of the object.  On the surface of the Earth, mass and weight are often interchanged.  In some places, objects are sold by the gram (mass), and in other locations, the same objects are sold by the ounce (weight).

The Weight Calculators use the dimensions of an object and its shape to compute the objects volume.  They then apply a density associated with a material to estimate the objects weight.

Weight Calculators

• Weight from Area, Height and Density
• Cube Weight 
• Box Weight
• Cone Weight
• Cone Frustum Weight
• Cylinder Weight
• Slanted Cylinder Weight
• Semicircle Weight
• Triangular Weight
• Quadrilateral Weight 
• Pentagon Weight 
• Hexagon Weight 
• Heptagon Weight
• Octagon Weight
• Nonagon Weight
• Decagon Weight
• Hendecagon Weight
• Dodecagon Weight
• Paraboloid Weight
• Polygon Pyramid Frustum Weight
• Sphere Mass
• Sphere Cap Weight
• Sphere Segment Weight
• Sphere Shell Mass
• Oblate Spheroid Mass
• Ellipsoid Weight
• Torus Weight
• Bottle Weight
• Bottle Content Weight
• Chamfer Weight
• Ring Weight