Ellipsoid Cap - Mass

The Mass or Weight of an Ellipsoid Cap calculator computes the mass or weight of an ellipsoid cap where the semi-axes of the ellipsoid are a, b, and c, and the height of the cap is h.  The mean density is also used.

INSTRUCTIONS:  Choose units and enter the following:

• (a)  semi-axis a.
• (b)  semi-axis b.
• (c)  semi-axis c.
• (h) height of the cap
• (mD) mean density of the cap material [CLICK HERE ]

Mass or Weight of an Ellipsoid Cap (M): The mass is returned in kilograms. However, the volume can be automatically converted to compatible units via the pull-down menu. 

The Math / Science

his calculator first computes the volume of an ellipsoid cap  based on the following formula:

           `V = π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))`

where:

• V is the volume of the ellipsoid cap
• a, b and c are the lengths of the semi-axes
• x = c - h and h is the height of the ellipsoid cap

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

        Mass = Volume ⋅ Density

To query the mean density (mD or μD) of many common substances, elements, liquids and materials, CLICK HERE (e.g. the density of water is 1,000 kg/m³.

When the formula for mass and volume of a Ellipsoid Cap are combined, one has formula for the mass of an ellipsoid cap is:

    M = `π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))⋅mD`

where:

• M is the mass of the ellipsoid cap 
• a, b and c are the lengths of the semi-axes
• x = c - h and h is the height of the ellipsoid cap
• mD is the mean density of the material

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.

Related Calculators:

• Volume of an Ellipsoid Cap
• Mass of an Ellipsoid Cap
• Volume of a Ellipsoid
• Weight or Mass of an Ellipsoid
• Surface Area of an Ellipsoid
• Volume of a Sphere
• Volume of a Oblate Spheroid