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Mathematics Question on Surface integral

The value of surface integral ∬S(9xi^−2j^−zk^).n^dS\iint_S(9x\hat{i}-2\hat{j}-z\hat{k}).\hat{n}dS over the surface S of the sphere x2+y2+z2=9 where n^\hat{n} is the unit outward normal to surface element dS is:

A

243\frac{24}{3}π

B

2163\frac{216}{3}π

C

216π

D

24π

Answer

216π

Explanation

Solution

The correct answer is(C): 216π