Chapter 8.2, Problem 31E

(a) The ellipse

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1a>b$

is rotated about the x-axis to form a surface called an ellipsoid, or prolate spheroid. Find the surface area of this ellipsoid.

(b) If the ellipse in part (a) is rotated about its minor axis (the y-axis), the resulting ellipsoid is called an oblate spheroid. Find the surface area of this ellipsoid.