Let R be the region enclosed by the graph of y=√x-1 and x=10 and the x axis

b) find the volume of the solid generated when R is revolved about the horizontal line y=3

I thought it would be

3.14 X the integral from 1 to 10 of (3)² - (3-√x-1)²

according to my answer key, it is instead

(3)² - (√x-1 -3)²

I really don't get this. 3 is above √x-1 so why wouldn't you do 3 - √x-1 instead of √x-1 -3 (which would give a negative number)

Please help guys, maybe my answer key is wrong?

Thanks.