Sphere Shell Mass

The Mass or Weight of a Spherical Shell calculator computes the volume of a spherical shell with an outer radius (r) and a thickness (t).    Spherical Shell INSTRUCTIONS: Choose your units (e.g. centimeters, inches or kilometers) and enter the following parameters:

• (r) Outer Radius of Sphere
• (t) Thickness of Sphere Shell
• (mD) Mean Density of Material in Shell

Mass of the Spherical Shell (M): The mass is returned in kilograms.  However the user can automatically convert the mass to other mass and weight units (e.g. grams, ounces, pound and tons) via the pull-down menu.  To compute the Volume of a Spherical Shell, CLICK HERE.

Uses

The mass of a spherical shell can compute the amount of materials needed to coat any spherical object from a candy gumball to a submarine bathysphere.  
To look-up the Mean Density of over 500 substances,CLICK HERE.

The Math

The equation calculate the Volume of a Sphere is V = 4/3•π•r³. This formula computes the difference between two spheres to represent a spherical shell, and can be algebraically reduced as as follows:

 V = 4/3 π (r³ - (r-t)³)

where:

• r is the outer radius and
• t is the thickness

Once the volume of the shell is known, this calculator then uses that volume with the mean density as follows:

• mass = mD • volume

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

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