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:
Mass or Weight of a Sphere Segment (m): The calculator returns the mass in kilograms. However, this can be automatically converted to other mass or weight units (e.g. pounds, tons) via the pull-down menu.
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.
The mean density (`mu_(density)`) of many common substances, elements, liquids and materials can be found by clicking HERE (e.g. the `mu_(density) (water)` is 1000.0 kg/m³).