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:
| Common Mean Densities | |
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Fluids
Fuels
Market-Ready Grains |
Metals
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Mean Density is the average amount of mass within a volume for a substance. Note, volume of a material is often highly subject to the temperatures, since materials expand as they warm. For that reason, mean densities of substances are often cited with a set of nominal conditions such as temperature and barometric pressure.
The formula for mean density is:
μD = V / m
where:
- μD = mean density
- V = Volume in units like cubic meters or cubic inches
- m = Mass in units like kilograms or pounds
Mean density is also often indicated as the Greek symbol rho (ρ).
Mass and Weight
Density is a function of mass. However, converting from mass to weight is trivial under the right conditions. Fortunately those conditions are generally true anywhere on the surface of the Earth, so the conversions built into the vCalc engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.
CLICK HERE for a pop-up function that provides the mean density (mD or μD) of many common substances, elements, liquids and materials.
Mean Density Units
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)
vCalc provides for automatic conversions between density units via the pull-down menus.
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