The area bounded by the parabola y=2x-x^2, the y-axis and the line y=1 is rotated about the X-axis. Find the volume generated.

Find the volume of the solid generated by the rotating the region bounded by the parabola y=1-x^2 and the lines x=1, y=1 about the X-axis.

For both of these questions I used the volume of revolution formula and integrated each respective equation and calculated it between x=1 and x=0.

For BOTH questions i got (8pi)/15 and for both questions, the answer says (7pi)/15. Could someone please point out where i have gone wrong? i realise that this area is a little unusual so maybe i am not working in the right angle. Please help me if you can. Thank You =)