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Answer:
340 degrees
Step-by-step explanation:
So the key thing here is to notice that we are given the circumference which will allow us to find a value for the radius of the circle and hence the angle subtended by the arc (the central angle).
So the circumference of a circle = 2pi(r)
This means:
6 = 2pi(r)
Which means that
r = 6/2pi or r = 3/pi
Now we can use this value of r to find our angle in conjunction with the value of the arc length. So:
Arc length is defined by: length = θr
Where θ is our angle value.
So lets plug in:
Multiply by pi to get:
Divide by 3 to get that:
θ = 17pi/9
So if we convert that from radians to degrees we get 340 degrees.
In the first octant, the given plane forms a triangle with vertices corresponding to the plane's intercepts along each axis.
Now that we know the vertices of the surface
, we can parameterize it by
where
and 
. The surface element is
With respect to our parameterization, we have
, so the surface integral is
Now that we know the vertices of the surface
where
With respect to our parameterization, we have