Question

The surface integral $\iint \frac{1}{\pi }(9x\hat{i}-8y\hat{j})\hat{n}ds$ over the sphere given by $x^2+y^2+z^2=9$ is_______

• A. 36

Answer 1

The correct option is A 36
$x^2+y^2+z^2=9$
According to gauss divergence theorem

${\iint }_s\frac{1}{\pi }(9xi-8y\hat{j})\hat{n}ds=\iiint \frac{1}{\pi }\left(divergence\right(9x\hat{i}-8y\hat{j}\left)\right).dv$

$=\frac{1}{\pi }[9-8]\times \frac{4\pi r^3}{3}{|}_{r=3}$

$=\frac{1}{\pi }\times 1\times \frac{4}{3}\pi \times 27=36$