Hi All,(adsbygoogle = window.adsbygoogle || []).push({});

I'm looking for help in converting 2D density (objects/area) in a circle to 3D density (objects/volume) in a sphere, the circle and sphere having the same radius and distribution of objects being uniform.

To make this problem more intuitive, here's a sample application: both crabs and fish forage on the same plankton in the water column. The crab can only access plankton as he walks on the ground (i.e., he forages in 2D space), but the fish can access the plankton in the water column (i.e., he forages in 3D space). The crab has a detection area of ∏*acuity^2 while the fish has a detection volume of (4/3)*∏*acuity^3. Given a prey density, can the number of prey within the 2D detection zone be converted to the number of prey within the 3D detection zone (or vice versa)?

I may be overthinking this, but help is much appreciated! Thanks!

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# Converting 2D density (circle) to 3D density (sphere)

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