Volume by Cylindrical shells

Question

The question states as follows:

Let $R$ be the region bounded by the curve $x=9y-y^2$ and the $y- axis$. Find the volume of the solid resulting from revolving $R$ about the line $y= -6$.

From my intent, i got $a$ and $b$ to be

$a = 0$

$b = 9$

Note: this problem is in the section of solving by cylindrical shells. I have set up:

$r(y) = y+6 $

$h(y) = 9y-y^2$

I am not sure if this is correct.

Can anyone help me please?

Thanks :)

Answer 1

$$ V =2π \int_ 0 ^ 9(3y^2-y^3+54y)dy$$

after that i got the answer to be $8015.7$