Question

Find the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

x^2+(y-5)^2=16 about the y axis.

Volume = __?__

Answer 1

so we have a donut pretty much

Answer 2

radius of 4; and we are 5 away from the center so yeah; a donut

Answer 3

shell method might be appicable

Answer 4

\[\int 2pix\ f(x)\ dx\]
\[f(x)=\sqrt{16-x^2}+5\]
\[4pi\int_{2}^{10}x\sqrt{16-x^2}+5x\ dx\]

Answer 5

one idea that might work, and be simpler is this: