Quit[]

(* Online calculator *)

"http://keisan.casio.com/exec/system/1311572253"

(* Axes *)

a=3;
b=2;
c=1;

(* Plot *)

mx=Max[a,b,c];

ContourPlot3D[(x^2)/a^2+(y^2)/b^2+(z^2)/c^2==1,{x,-mx,mx},{y,-mx,mx},{z,-mx,mx}]

(* Volume *)

N[4/3 Pi a b c,14]

(* Three formulas for the Area *)

e1=(Sqrt[1-c^2/a^2]);
e2=(Sqrt[1-c^2/b^2]);
k=e2/e1;

8a b*NIntegrate[(Sqrt[1-e1^2 s^2])EllipticE[e2^2 (((1-s^2))/(1-e1^2 s^2))],{s,0,1},WorkingPrecision->40,AccuracyGoal->40,PrecisionGoal->40]

N[2Pi (c^2+ ((b c^2)/(Sqrt[a^2-c^2]))EllipticF[ArcSin[(Sqrt[1-c^2/a^2])],k^2]+b (Sqrt[a^2-c^2])EllipticE[ArcSin[(Sqrt[1-c^2/a^2])],k^2]),40]

N[2Pi (c^2+ ((b c^2)/(Sqrt[a^2-c^2]))InverseJacobiSN[e1,k^2]+b (Sqrt[a^2-c^2])EllipticE[JacobiAmplitude[InverseJacobiSN[e1,k^2],k^2],k^2]),40]