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.
x2 + (y - 22 = 4; about the y-axis

Answer 1

$x^2+(y-2)^2=4\implies y=2\pm\sqrt{4-x^2}$

describes a circle of radius 2 centered at (0,2). A revolution of this region about the y-axis would give you a sphere of radius 2, so the volume would be $\dfrac43\pi\times2^3=\dfrac{32}3\pi$.