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Mathematical analysis demonstrates an elementary derivation of sphere volume via geometric decomposition, suggesting a viable alternative to standard calculus techniques.
This paper provides a compact and elementary derivation of the volume of a sphere by means of geometric decomposition technique. With the help of such a decomposition technique, the sphere is divided into certain geometric pieces that give an immediate derivation of the volume formula of a sphere, V = 4/3π r³. This seven-page proof can be regarded as an alternative to conventional derivations using Calculus.
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Asser Mohamed Fathy Abd Elnaby Heweage (2026) studied this question.
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