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 − 4)^2 = 16; about the y-axis

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 − 4)² = 16;    about the y-axis

V=?

Answer 1

The graph of x² + (y - 4)² = 16 is the circle with center (0,4) and radius 4.

If the curve is rotated about the y'axis, a sphere with center (0,4) and radius 4 is generated.

So, the volume, V, of the resulting solid is (4/3)π(4)³ = 256π/3.