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
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 .
your radius is incorrect,
you have to subtract the volume calculated using
from the volume calculated using r=2.
Your volume of rotation using washers is the difference between 2 volumes of rotation.
No, the length you calculated is the width of the washer at any height y.
That's the distance between the pink circles.
As the shape is being revolved around the y axis,
you have 2 radii, one outer radius=2 and one inner radius =
Hence you must calculate