A volume integral over a sphere

[advphys]

Homework Statement

∫∫∫∇.Fdv over x²+y²+z²≤25

F= (x²+y²+z²)(xi+yj+zk)

Homework Equations

∫∫∫∇.Fdv = ∫∫ F.n dσ

n=∇g/|∇g|

The Attempt at a Solution

g(x,y,z)=x²+y²+z²-25

taking the surface integral and replacing all
(x²+y²+z²) with 25
i got
125 * ∫∫ dσ = 12500π

But the answer key says it is 100π
I think i am making a mistake with numbers but, i couldn't find what is wrong.

Thanks

 

[LCKurtz]

I don't think anything is wrong except the answer key.

 

[advphys]

Hmm, ok then, thanks.