Question

Find the volume of the solid when rotated about the y-axis.
y=3-x^2/9
x=3
the answer is 45/2 pi
can you show me how to get that answer? thank you

Answer 1

If you are rotating about the \(y\) axis, you want the function in terms of \(x\).

Answer 2

Then you want to integrate with respect to \(y\).

Answer 3

integrate from x=0 to x=3

Answer 4

\[
y=3-\frac{x^2}{9}\implies x^2 = 9(3-y) = 27-9y
\]

Answer 5

so x^2= -9y+27
and x=3