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 − 4)^2 = 16; about the y-axis

Answer 1

for
(x-h)^2+(y-k)^2=r^2
center is (h,k) and radius is r

we have
(x-0)^2+(y-4)^2=4^2

that's a circle
it is centered at (0,4)
radius is 4
around the y axis
means we get a sphere
radius is 4
V=(4/3)pir^3
V=(4/3)pi4^3
V=(4/3)pi64
V=(256/3)pi units³ or aprox 268.08257 units³
see attachment