4/7 of the birthday cake was eaten on your birthday. the next day your dad ate 1/2 of what was left. you get to finish the cake,
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Assuming 
does not include the plane 
, we can parameterize the region in spherical coordinates using
where
and 
. We then have
Then the surface integral is equivalent to
We have
So the surface integral is equivalent to
where
.
where
Then the surface integral is equivalent to
We have
So the surface integral is equivalent to
where