Question Number 23393 by ajfour last updated on 29/Oct/17
$${Show}\:{that}\:{volume}\:{of}\:{a}\:{region} \\ $$$${of}\:{space}\:{bounded}\:{by}\:{a}\:{boundary} \\ $$$${surface}\:{S}\:{is}\:\:{V}=\:\frac{\mathrm{1}}{\mathrm{3}}\underset{{S}\:} {\int\int}{r}\mathrm{cos}\:\theta{dA}\:. \\ $$$$\theta\:{being}\:{the}\:{angle}\:{between}\:{the} \\ $$$${position}\:{vector}\:{of}\:{a}\:{point}\:{P}\:\:{on} \\ $$$${the}\:{surface},\:{and}\:{the}\:{outer}\:{normal} \\ $$$${to}\:{the}\:{surface}\:{at}\:{P}. \\ $$$${r}\:{is}\:{the}\:{distance}\:{of}\:{point}\:{P}\:{from} \\ $$$${origin}. \\ $$
Commented by ajfour last updated on 07/Nov/19
$$? \\ $$