I have two questions here, the first i need someone to show me my mistake somewhere, the second I have no idea how to do.

1. The area defined by the inequalities

,

is rotated about the y-axis. Find the volume generated.

I take the raduis of the figure generated from the y-axis outward. so then its value would be

This rotates the region under the curve, you should be rotating the region above it.
answer is

2. Find the volume generated when the area in the first quadrant enclosed by

, and the line y=1 is rotated about the line y=1.

I only know that the lines intersect at x=0 and

. Also the radii of the figure would be

.

Thanks!