🧄Total Mass in a Cube vs. a Sphere

The total mass of an object is determined by integrating its density function over its volume, and this process is significantly influenced by the chosen coordinate system (e.g., Cartesian for a cube versus spherical for a sphere) and the shape's symmetry. The animation effectively highlights this by showing how the same distance-dependent density function yields distinct total mass values when applied to different geometries like a cube and a sphere. This emphasizes the interplay between geometry and density distribution in determining an object's overall mass.

🎬how to calculate mass in a non-uniform density field by using volume integration

The animation cycles between two different volumes: a cube and a sphere. This feature directly addresses the two parts of the problem and allows for a direct comparison of the results. You can see how the same density function, when integrated over different shapes, yields two distinct total mass values. The on-screen text updates to display the calculated mass for each volume, reinforcing the final answers derived in the analysis.

🖊️Mathematical Proof

Total Mass in a Cube vs. a Sphere | Proof and Derivationviadean on Notion