A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball). If the minor axis is chosen, the surface is called an oblate spheroid (similar to the shape of the planet Earth). 
 Prolate spheroid.
 

 Oblate spheroid.
 The sphere is a special case of the spheroid in which the generating ellipse is a circle. A spheroid is a special case of an ellipsoid where two of the three major axes are equal.
Volume Prolate spheroid: Oblate spheroid: where  a is the major axis length
 b is the minor axis length
Surface area A prolate spheroid has surface area An oblate spheroid has surface area  2πb(b + aˇarcsin(e)/e).
Here e is the eccentricity of the ellipse, defined as 