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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

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LammettHash

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

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 \(\dfrac43\pi\times2^3=\dfrac{32}3\pi\).

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