VC5.47

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Using divergence theorm,we get

\iint _{S}xdydz=\iiint _{V}{\frac  {\partial }{\partial x}}(x)dxdydz=\iiint _{V}dV=V\,

Similarly,\iint _{S}ydzdx=V,\iint _{S}zdxdy=V\,

Adding these three,we have

\iint _{S}(xdydz+ydzdx+zdxdy)=3V\,

Therefore,{\frac  {1}{3}}\iint _{S}(xdydz+ydzdx+zdxdy)=V\,

Hence the required is proved.

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