Chapter 8.2, Problem 31E

1. (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.
2. (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.