Unexpected integration result in Wolfram|Alpha?

Hello All,

I’m working on a problem which I’m currently stuck on.
I would like to calculate the volume of fluid in a horizontal end cap.

(here k =1 and r = 1.5)

What i do is:
Get the describing equation.

Then rotate it along the x axis. This gives a circle over the x axis on any given point on the curve.
And finally integrate over the y axis. To get the volume.

Unfortunately if I put in numbers for k and r and try to compute the volume with y i don’t get the correct results.
A full volume with k =1 and r=1.5 should give me: 22.88.
What have I done wrong?

Hello,
Same happened here,
but with a much simpler integral,
though it’s not technically a simple but a double integral,
please see the attached screenshot..