WOLFRAM|DEMONSTRATIONS PROJECT

Approximating Volumes by Summation

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shape
sphere
cone
Steinmetz
number of layers
layer opacity
layer sample
bottom
middle
top
layer color
show shape
shape opacity
shape color
approximate volume:
4.24697
exact volume:
4.18879
The volume of a solid shape can be approximated by slicing it into layers and summing the volumes of all of the layers. The limit of this process is an integral that yields the volume of the solid. This is an analogue of a Riemann summation of the area under a curve.