Consider the cardioid in R² defined by the polar equation
r=1+sinθ
a. Find the volume of the solid obtained by revolving this curve about the y-axis.
b. Find the area of the surface obtained by revolving this curve about the y-axis.
Hint: The given cardioid is symmetric about the y-axis. To generate a solid or a surface by revolving about the y-axis, we only need the right-half of the cardioid.