Question

The surface integral${\iint }_s\frac{1}{\pi }(9xi-3yj).nds$ over the sphere given by $x^2+y^2+z^2=9$is_______

• A. 216

Answer 1

The correct option is A 216
By Gauss Divergence theorem,

${\iint }_s\overrightarrow{F}.\overrightarrow{n}ds={\iiint }_v(\nabla .\overrightarrow{F}).dV$

${\iint }_s\frac{1}{\pi }(9x\hat{i}-3y\hat{j}).nds=\frac{6}{\pi }{\int }_{v}dV$

$=\frac{6}{\pi }\times V=\frac{1}{\pi }\times 6\times \frac{4\pi }{3}(3{)}^3$

=216