Question

The region bounded by the given curve is rotated about the specified axis. Find the volume V of the resulting solid by any method. x^2 + (y − 2)^2 = 4; about the y-axis

Answer 1

X^2+(y-2)^2=4 is a circle centered at (0,2) with radius 2.
Thus, when you rotate it around the y-axis (around x=0),
you get a sphere with radius 2.

((which is centered at (x,y,z)=(0,2,0), if you take y to be
the vertical axis ... not that you need to know this for volume))

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Volume of a sphere formula: V = (4/3)πr^3.