Math Help - Volume around the y-axis

1. Volume around the y-axis

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y = x^2 and y = 9 about the y axis.

My first answer was 54, my second 18. Neither are correct, but I feel at a loss for this problem.

2. Have you learned the disk method for finding a volume of a solid of revolution? You have a vertical axis of revolution so you'll have to rewrite the function $y = x^2$ in terms of x -> $x = \sqrt{y}$.

The integral to set up is
$V = \pi \displaystyle \int_c^d [R(y)]^2 dy$

Plug in $\sqrt{y}$ for R(y), 0 for c, and 9 for d:

$V = \pi \displaystyle \int_0^9 (\sqrt{y})^2 dy$

Take it from here.

3. I had not learned this method (or many others). I'm in the process of teaching myself Calc I out of a textbook and so I'm having a hard time connecting some of the dots. Let me work this real quick...127.23.

Thank you!