Finding region between the graph and x-axis and volume by turning around x-axis 360degree

[cloudy1290]

Given equation : x=α−sin(α) and y=1−cos⁡(α) and 0⩽α⩽2π

Find
1.region between the graph and the x axis
2.volume of the graph which is made by turning the graph around x-axis 360degree

my solution :
1. integral of (1−cosα)^2 dα from 0 to 2π = 3π
2. π * integral of (1−cosα)^3 dα from 0 to 2π = 5π^2

are these answer correct?

 

[MarkFL]

Yes, those are correct answers.