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 Recognitions: Homework Help Gauss's theorem states: $$\int_A (\nabla \cdot \vec F) dV = \int_{\partial A} \vec F \cdot d \vec A$$ Where $A$ is a volume in space and $\partial A$ is its bounding surface. If you can find a vector function $\vec F$ with $\nabla \cdot \vec F=1$, then the LHS, and so also the RHS, is equal to the volume of A.